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TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS
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作者 瘳军 郑大彬 刘合国 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1769-1775,共7页
The well-known tower theorem of groups (resp. Lie algebras) shows that the tower of automorphism groups (resp. derivation algebras) of a finite group (resp. a finite dimensional Lie algebra) with trivial center ... The well-known tower theorem of groups (resp. Lie algebras) shows that the tower of automorphism groups (resp. derivation algebras) of a finite group (resp. a finite dimensional Lie algebra) with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete. 展开更多
关键词 Lie rings derivation towers complete Lie rings
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Cocentralizing Generalized Derivations in Prime Rings 被引量:1
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作者 马晶 徐晓伟 《Northeastern Mathematical Journal》 CSCD 2006年第1期105-113,共9页
Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D(x)x - xG(x) ∈ Z for all x ∈S. The main purpose of this paper is to describe the structur... Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D(x)x - xG(x) ∈ Z for all x ∈S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime ease is also considered. 展开更多
关键词 prime ring derivation generalized derivation cocentralizing mapping
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The Linear Combination of Derivations in Prime Rings 被引量:5
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作者 王宇 张秀英 《Northeastern Mathematical Journal》 CSCD 2002年第4期298-302,共5页
In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bre... In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bresar and obtain a lemma that is of independent interest. 展开更多
关键词 derivation prime ring extended centroid
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Generalized Derivations in Prime Rings
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作者 吴伟 宛昭勋 《Transactions of Tianjin University》 EI CAS 2011年第1期75-78,共4页
Let R be a ring, a ,b ∈ R, ( D , α ) and (G , β ) be two generalized derivations of R . It is proved that if aD ( x ) = G ( x )b for all x ∈ R, then one of the following possibilities holds: (i) If either a or b i... Let R be a ring, a ,b ∈ R, ( D , α ) and (G , β ) be two generalized derivations of R . It is proved that if aD ( x ) = G ( x )b for all x ∈ R, then one of the following possibilities holds: (i) If either a or b is contained in C , then α = β= 0 and there exist p , q ∈ Qr ( RC) such that D ( x )= px and G ( x )= qx for all x ∈ R;(ii) If both a and b are contained in C , then either a = b= 0 or D and G are C-linearly dependent;(iii) If neither a nor b is contained in C , then there exist p , q ∈ Qr ( RC) and w ∈ Qr ( R) such that α ( x ) = [ q ,x] and β ( x ) = [ x ,p] for all x ∈ R, whence D ( x )= wx-xq and G ( x )= xp + avx with v ∈ C and aw-pb= 0. 展开更多
关键词 prime ring right Martindale quotient ring extended centroid generalized derivation
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Compositions of Generalized Derivations in Prime Rings
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作者 马晶 徐晓伟 《Northeastern Mathematical Journal》 CSCD 2008年第4期354-362,共9页
Let R be a prime ring with a non-central Lie ideal L. In the present paper we show that if the composition DG of two generalized derivations D and G is zero on L, then DG must be zero on R. And we get all the possibil... Let R be a prime ring with a non-central Lie ideal L. In the present paper we show that if the composition DG of two generalized derivations D and G is zero on L, then DG must be zero on R. And we get all the possibilities for the composition of a couple of generalized derivations to be zero on a non-central Lie ideal of a prime ring. 展开更多
关键词 prime ring generalized derivation COMPOSITION
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Left Annihilator of Power Values with Derivations on Lie Ideals in Prime Rings
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作者 HUANG Shu-liang 《Chinese Quarterly Journal of Mathematics》 2020年第2期179-185,共7页
Let R be a prime ring with characteristic di erent from two,d a derivation of R,L a noncentral Lie ideal of R,and a2R.In the present paper it is showed that if a(d(u^m)±u^m)^n for all u∈L,where m;n are xed posit... Let R be a prime ring with characteristic di erent from two,d a derivation of R,L a noncentral Lie ideal of R,and a2R.In the present paper it is showed that if a(d(u^m)±u^m)^n for all u∈L,where m;n are xed positive integers,then a=0 unless R satis es s4,the standard polynomial identity in four variables. 展开更多
关键词 derivation Extended centroid Lie ideal Prime ring
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Annihilator on Co-commutators with Derivations on Lie Ideals in Prime Rings
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作者 吴伟 牛凤文 《Northeastern Mathematical Journal》 CSCD 2006年第4期415-424,共10页
Let R be a prime ring of characteristic different from 2, d and 9 two derivations of R at least one of which is nonzero, L a non-central Lie ideal of R, and a ∈ R. We prove that if a(d(u)u - ug(u)) = 0 for any... Let R be a prime ring of characteristic different from 2, d and 9 two derivations of R at least one of which is nonzero, L a non-central Lie ideal of R, and a ∈ R. We prove that if a(d(u)u - ug(u)) = 0 for any u ∈ L, then either a = O, or R is an sa-ring, d(x) = [p, x], and g(x) = -d(x) for some p in the Martindale quotient ring of R. 展开更多
关键词 prime ring generalized polynomial identity differential identity
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Rising utilization of stable isotopes in tree rings for climate change and forest ecology 被引量:1
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作者 Ru Huang Chenxi Xu +3 位作者 Jussi Grießinger Xiaoyu Feng Haifeng Zhu Achim Bräuning 《Journal of Forestry Research》 SCIE EI CAS CSCD 2024年第1期103-116,共14页
Analyses of stable isotopes(C,O,H)in tree rings are increasingly important cross-disciplinary programs.The rapid development in this field documented in an increasing number of publications requires a comprehensive re... Analyses of stable isotopes(C,O,H)in tree rings are increasingly important cross-disciplinary programs.The rapid development in this field documented in an increasing number of publications requires a comprehensive review.This study includes a bibliometric analysis-based review to better understand research trends in tree ring stable isotope research.Overall,1475 publications were selected from the Web of Science Core Collection for 1974-2023.The findings are that:(1)numbers of annual publications and citations increased since 1974.From 1974 to 1980,there were around two relevant publications per year.However,from 2020 to 2022,this rose sharply to 109 publications per year.Likewise,average article citations were less than four per year before 1990,but were around four per article per year after 2000;(2)the major subjects using tree ring stable isotopes include forestry,geosciences,and environmental sciences,contributing to 42.5%of the total during 1974-2023;(3)the top three most productive institutions are the Chinese Academy of Sciences(423),the Swiss Federal Institute for Forest,Snow and Landscape Research(227),and the University of Arizona(204).These achievements result from strong collaborations;(4)review papers,for example,(Dawson et al.,Annu Rev Ecol Syst 33:507-559,2002)and(McCarroll and Loader,Quat Sci Rev 23:771-801,2004),are among the most cited,with more than 1000 citations;(5)tree ring stable isotope studies mainly focus on climatology and ecology,with atmospheric CO_(2) one of the most popular topics.Since 2010,precipitation and drought have received increasing attention.Based on this analysis,the research stages,key findings,debated issues,limitations and direc-tions for future research are summarized.This study serves as an important attempt to understand the progress on the use of stable isotopes in tree rings,providing scientific guid-ance for young researchers in this field. 展开更多
关键词 Tree rings Stable isotopes Web of Science BIBLIOMETRIC
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Cover story: Neuromodulation Brings Sunshine to Diseased Brains
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《General Psychiatry》 CSCD 2024年第1期32-32,共1页
Various invasive and non-invasive brain modulation methods are widely used to regulate sensory,cognitive,and motor functions both within local and large brain networks.This special issue provides innovative studies to... Various invasive and non-invasive brain modulation methods are widely used to regulate sensory,cognitive,and motor functions both within local and large brain networks.This special issue provides innovative studies to optimize relevant methods and understand their neural mechanisms,paving the way for personalized neuromodulation of cognitive function.The cover of this issue uses the image of the four heavenly Kings in Chinese culture who are in charge of good weather.It compares the process of neuroregulation technology that integrates the principles of sound,light electricity or magnetism in treating the diseased brain,to the moment when these gods cast their spells to bring sunshine and peace to the human brain in the midst of lightning and thunder. 展开更多
关键词 SUNSHINE LIGHTNING rings
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Characterizations of semihoops based on derivations
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作者 WANG Mei ZHANG Xiao-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期291-310,共20页
In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multipli... In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence. 展开更多
关键词 (prelinear)semihoop derivation Heyting algebra Galois connection
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Effectivity and safety of trifocal intraocular lenses and capsular tension rings implantation for cataract patients with axial high myopia
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作者 Shan Hua Qiu-Xia Xie +1 位作者 Hu Wang Jing-Xiang Zhong 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2024年第3期499-508,共10页
●AIM:To assess effectivity and safety of trifocal intraocular lenses(IOLs)and capsular tension rings in treating cataract patients with axial high myopia.●METHODS:A prospective nonrandomized controlled clinical tria... ●AIM:To assess effectivity and safety of trifocal intraocular lenses(IOLs)and capsular tension rings in treating cataract patients with axial high myopia.●METHODS:A prospective nonrandomized controlled clinical trial was conducted.Totally 98 eyes(74 patients)who underwent femtosecond laser-assisted cataract surgery(FLACS)with trifocal IOLs were enrolled in the study and followed up for 2y after surgery:46 eyes(33 patients)with capsular tension ring implantation in the long axial lengths(AL)group(26<AL<29 mm)and 52 eyes(41 patients)in the normal AL group(22<AL<24.5 mm).Postoperative outcomes about effectivity and safety,including the subjective and objective visual quality,and postoperative complications were assessed.●RESULTS:Uncorrected distance visual acuity at 5 m and uncorrected intermediate visual acuity at 60 and 80 cm in the long AL group were significantly worse than those in the normal AL group at 3mo postoperatively(P<0.05).The differences in reading speed,spectacle independence and potential visual complaints between the two groups were not statistically significant(P>0.05).The dysfunctional lens index and total modulation transfer function(MTF)average height were similar between the two groups.The postoperative internal coma aberrations in the axial high myopia eyes were significantly higher than that in the normal AL group(P<0.05).The total satisfaction score in the long AL group(91.32±2.76)was slightly higher than that in the normal AL group(90.36±3.47),but there was no difference(P=0.136).A statistically negative correlation was found between corrected distance visual acuity(CDVA)and dysfunctional lens index(r=-0.382,P=0.009),and between CDVA and the total MTF average height(r=-0.374,P=0.01).But there was no significant correlation between CDVA and total satisfaction score(r=0.059,P=0.696).Postoperative complications mainly presented as posterior capsular opacity(PCO),retinal detachment and cystoid macular edema.There was no difference in the incidence of fundus disease(6.5%vs 3.8%,P=0.663)or PCO(17.4%vs 7.7%,P=0.217)between the two groups at two years.●CONCLUSION:The utilization of trifocal IOL and capsular tension ring implantation is beneficial for cataract patients with axial high myopia undergoing FLACS.This approach not only ensures excellent subjective feelings and objective visual quality,but also does not increase the incidence of postoperative complications. 展开更多
关键词 trifocal intraocular lenses capsular tension ring axial high myopia CATARACT visual quality
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Weak M-Armendariz rings
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作者 张翠萍 陈建龙 《Journal of Southeast University(English Edition)》 EI CAS 2009年第1期142-146,共5页
For a monoid M, this paper introduces the weak M- Armendariz rings which are a common generalization of the M- Armendariz rings and the weak Armendariz rings, and investigates their properties. Moreover, this paper pr... For a monoid M, this paper introduces the weak M- Armendariz rings which are a common generalization of the M- Armendariz rings and the weak Armendariz rings, and investigates their properties. Moreover, this paper proves that: a ring R is weak M-Armendariz if and only if for any n, the n-by-n upper triangular matrix ring Tn (R) over R is weak M- Armendariz; if I is a semicommutative ideal of ring R such that R/I is weak M-Armendariz, then R is weak M-Armendariz, where M is a strictly totally ordered monoid; if a ring R is semicommutative and M-Armendariz, then R is weak M × N- Armendariz, where N is a strictly totally ordered monoid; a finitely generated Abelian group G is torsion-free if and only if there exists a ring R such that R is weak G-Armendariz. 展开更多
关键词 semicommutative rings M-Armendariz rings weak Armendariz rings weak M-Armendariz rings
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(ρ, τ, σ)-Derivations of Dendriform Algebras
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作者 Yousuf A. Alkhezi 《Applied Mathematics》 2023年第12期839-846,共8页
We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provid... We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras. 展开更多
关键词 Dendriform Algebras derivationS Generalized derivations
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An Introduction to the Theory of Matrix Near-Rings
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作者 Saviour Chibeti Iness Kyapwanyama 《Advances in Pure Mathematics》 2023年第2期71-95,共25页
Matrix rings are prominent in abstract algebra. In this paper we give an overview of the theory of matrix near-rings. A near-ring differs from a ring in that it does not need to be abelian and one of the distributive ... Matrix rings are prominent in abstract algebra. In this paper we give an overview of the theory of matrix near-rings. A near-ring differs from a ring in that it does not need to be abelian and one of the distributive laws does not hold in general. We introduce two ways in which matrix near-rings can be defined and discuss the structure of each. One is as given by Beildeman and the other is as defined by Meldrum. Beildeman defined his matrix near-rings as normal arrays under the operation of matrix multiplication and addition. He showed that we have a matrix near-ring over a near-ring if, and only if, it is a ring. In this case it is not possible to obtain a matrix near-ring from a proper near-ring. Later, in 1986, Meldrum and van der Walt defined matrix near-rings over a near-ring as mappings from the direct sum of n copies of the additive group of the near-ring to itself. In this case it can be shown that a proper near-ring is obtained. We prove several properties, introduce some special matrices and show that a matrix notation can be introduced to make calculations easier, provided that n is small. 展开更多
关键词 NEAR-rings First Near-Ring Isomorphism Zero Symmetric Near-Ring Near-Ring Module and Matrix Near-rings
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Some results on derivations of MV-algebras 被引量:1
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作者 WANG Jun-tao HE Peng-fei SHE Yan-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第1期126-143,共18页
In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations an... In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316]. 展开更多
关键词 MV-ALGEBRA derivation fixed point set IDEAL Boolean algebra
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β-Ga_(2)O_(3) junction barrier Schottky diode with NiO p-well floating field rings
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作者 何启鸣 郝伟兵 +6 位作者 李秋艳 韩照 贺松 刘琦 周选择 徐光伟 龙世兵 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期73-79,共7页
Recently,β-Ga_(2)O_(3),an ultra-wide bandgap semiconductor,has shown great potential to be used in power devices blessed with its unique material properties.For instance,the measured average critical field of the ver... Recently,β-Ga_(2)O_(3),an ultra-wide bandgap semiconductor,has shown great potential to be used in power devices blessed with its unique material properties.For instance,the measured average critical field of the vertical Schottky barrier diode(SBD)based onβ-Ga_(2)O_(3) has reached 5.45 MV/cm,and no device in any material has measured a greater before.However,the high electric field of theβ-Ga_(2)O_(3) SBD makes it challenging to manage the electric field distribution and leakage current.Here,we showβ-Ga_(2)O_(3) junction barrier Schottky diode with NiO p-well floating field rings(FFRs).For the central anode,we filled a circular trench array with NiO to reduce the surface field under the Schottky contact between them to reduce the leakage current of the device.For the anode edge,experimental results have demonstrated that the produced NiO/β-Ga_(2)O_(3) heterojunction FFRs enable the spreading of the depletion region,thereby mitigating the crowding effect of electric fields at the anode edge.Additionally,simulation results indicated that the p-NiO field plate structure designed at the edges of the rings and central anode can further reduce the electric field.This work verified the feasibility of the heterojunction FFRs inβ-Ga_(2)O_(3) devices based on the experimental findings and provided ideas for managing the electric field ofβ-Ga_(2)O_(3) SBD. 展开更多
关键词 gallium oxide Schottky barrier diode nickel oxide floating field rings
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AusMed Brings Game-Changing Healthcare Innovations from Hong Kong,China to the World——An interview with Christine Yip,Founder and CEO of AusMed Global Limited
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作者 Guo Yan 《China's Foreign Trade》 2023年第4期23-26,共4页
“As a non-invasive alternative to the traditional finger-prick blood ketone testing devices,boasting a high level of accuracy comparable to industrial gold standards typically attainable only through bulky and expens... “As a non-invasive alternative to the traditional finger-prick blood ketone testing devices,boasting a high level of accuracy comparable to industrial gold standards typically attainable only through bulky and expensive specialty equipment,we proudly introduce the world’s first-of-its-kind handheld breath ketone(BrAce)analyser,empowered by our patented disruptive photonic sensing technologies.These innovations are aimed at providing a more effective approach to managing diabetes and ketosis(fat metabolism),”said Christine Yip,founder and CEO of AusMed Global Limited,during a recent interview with China’s Foreign Trade magazine. 展开更多
关键词 KETONE rings typically
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Derivations of Certain Lie Algebras of Upper Triangular Matrices over Commutative Rings 被引量:8
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作者 王登银 於遒 偶世坤 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2007年第3期474-478,共5页
Let R be an arbitrary commutative ring with identity. Denote by t the Lie algebra over R consisting of all upper triangular n by n matrices and let b be the Lie subalgebra of t consisting of all matrices of trace 0. T... Let R be an arbitrary commutative ring with identity. Denote by t the Lie algebra over R consisting of all upper triangular n by n matrices and let b be the Lie subalgebra of t consisting of all matrices of trace 0. The aim of this paper is to give an explicit description of the derivation algebras of the Lie algebras t and b, respectively. 展开更多
关键词 derivations of Lie algebras commutative rings
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On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras
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作者 ZHU Hua ZHAO Jian-bin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第2期274-292,共19页
A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-L... A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements. 展开更多
关键词 derivation Boolean element Lattice implication algebra(LIA) 2-dimension linguistic lattice implication algebra(2DL-LIA) 2-dimension fuzzy linguistic information
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Commutativity of Near-rings with Derivations 被引量:1
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作者 Ahmed A.M. Kamal Khalid H. AI-Shaalan 《Algebra Colloquium》 SCIE CSCD 2014年第2期215-230,共16页
In this paper we first prove that a near-ring admits a derivation if and only if it is zero-symmetric. Also, we prove some commutativity theorems for a non-necessarily 3-prime near-ring R with a suitably-constrained d... In this paper we first prove that a near-ring admits a derivation if and only if it is zero-symmetric. Also, we prove some commutativity theorems for a non-necessarily 3-prime near-ring R with a suitably-constrained derivation d satisfying the condition that d(a) is not a left zero-divisor in R for some a ∈ R. As consequences, we generalize several commutativity theorems for 3-prime near-rings admitting derivations. 展开更多
关键词 NEAR-rings derivationS 3-prime near-ring non-left zero-divisors commuta-tivity of near-rings
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