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The Jacobson Radical of (R(G])~G
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作者 HUChang-liu WANGYuan-zheng 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第2期209-212,共4页
In this paper,the Jacobson radical of (R[G])^G, the fixed point subring of a group ring (R[G]) is studied. Some related properties of (R[G])^G are discussed.
关键词 G-ring group ring fixed point subring jacobson radical J-semisimple ring
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TENSOR PRODUCTS OF JACOBSON RADICALS IN NEST ALGEBRAS
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作者 DONG ZHE Departinent of Mathematics, Zhejiang University, Hangzhou 310027, China. Institute of Mathematics, Fudan University, Shanghai 200433, China. 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第3期323-330,共8页
This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,i... This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous. 展开更多
关键词 jacobson radical Tensor product Nest algebra
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The Jacobson and Brown-McCoy Radicals of Certain Group Rings
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作者 周永新 《Chinese Quarterly Journal of Mathematics》 CSCD 1995年第3期91-96,共6页
In this paper, we determine the Jacobson radicals and Brown-McCoy radicals of group rings of certain non-abelian groups and generalize some known results.
关键词 group rings jacobson radicals Brown-McCoy radicals nilpotent groups Frobenius groups
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On_λ[S] Semigroup of Semigroup
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作者 黄骏敏 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第2期1-4, ,共4页
In this paper,we introduce the notion of λ[S]([S] ρ) semigroup with the inner left and right translations of semigroup S,hence define the homomorphic mapping λ from λ[S] to S and we have λ[S]/kerλS λS and λ(J(... In this paper,we introduce the notion of λ[S]([S] ρ) semigroup with the inner left and right translations of semigroup S,hence define the homomorphic mapping λ from λ[S] to S and we have λ[S]/kerλS λS and λ(J( λ[S])=J(S λ),J(S λ) is the Jacobson radical of S λ. 展开更多
关键词 SEMIGROUP left(right) translations homomorphic mapping jacobson radical
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The Upper Radical Determined by the Class of all J-Semisimple Subdirectly Irreducible Rings
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作者 杨宗文 王俊民 《Journal of Mathematical Research and Exposition》 CSCD 2000年第4期503-506,共4页
F.A.Szasz has put forward the open problem 55 in [1]: Let K be the class of all subdirectly irreducible rings, whose Jacobson radical is (0). Examine the upper radical determined by the class K. In this paper, the pro... F.A.Szasz has put forward the open problem 55 in [1]: Let K be the class of all subdirectly irreducible rings, whose Jacobson radical is (0). Examine the upper radical determined by the class K. In this paper, the problem has been examined. (1) It has been proved that the upper radical R determined by the class K is a special radical,which lies between Jacobson radical and Brown-McCoy radical. (2) It has been given some necessary and sufficient condition of ring A to be an R-radical ring. 展开更多
关键词 subdirectly irreducible ring special radical antisimple radical MHR-ring jacobson radical.
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On Radicals of Skew Inverse Laurent Series Rings 被引量:1
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作者 A. Moussavi 《Algebra Colloquium》 SCIE CSCD 2016年第2期335-346,共12页
Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J(R[x]) of the polynomial ring R[x] is the polynomial ring over the nil ideal J(R[x])∩R. Following Amitsur, it is shown that wh... Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J(R[x]) of the polynomial ring R[x] is the polynomial ring over the nil ideal J(R[x])∩R. Following Amitsur, it is shown that when R is an Armendaxiz ring of skew inverse Laurent series type and S is any one of the ring extensions R[x; α], R[x,x^-1;α], R[[x^-1;α]] and R((x^-1; α)), then (S) = (R)S = Nil(S), (S) ∩ R = Nil(R), where is a radical in a class of radicals which includes the Wedderburn, lower nil, Levitzky and upper nil radicals. 展开更多
关键词 skew inverse Laurent series ring nil radical jacobson radical
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Classical Radicals of Invariants of Algebraic Skew Derivations
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作者 Jeffrey Bergen Piotr Grzeszczuk 《Algebra Colloquium》 SCIE CSCD 2022年第1期53-66,共14页
Let σ be an automorphism and δ be a q-skew σ-derivation of an F-algebra A.We prove that if A is semiprimitive and δ is algebraic,then the subalgebra A^(δ)={r∈A|δ(r)=0}has nilpotent Jacobson radical.Using this r... Let σ be an automorphism and δ be a q-skew σ-derivation of an F-algebra A.We prove that if A is semiprimitive and δ is algebraic,then the subalgebra A^(δ)={r∈A|δ(r)=0}has nilpotent Jacobson radical.Using this result,we obtain similar relations for the Baer prime radical,the Levitzki locally nilpotent radical,and the Kothe nil radical when the field F is uncountable.Then we apply it to actions of the n^(2)-dimensional Taft Hopf algebra T_(n2)(q)and the q-analogue U_(q)(sl(2))of the enveloping algebra of the Lie algebra sl(2). 展开更多
关键词 skew derivations INVARIANTS jacobson radical
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Pseudo-Injective Modules and Principally Pseudo-Injective Modules 被引量:4
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作者 杜先能 赵春娥 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2007年第2期223-228,共6页
Considered in this paper are pseudo-injective modules and principally pseudoinjective modules, which are generalizations of quasi-injective modules and PQ-injective modules. Pseudo-injective modules are dual to pseudo... Considered in this paper are pseudo-injective modules and principally pseudoinjective modules, which are generalizations of quasi-injective modules and PQ-injective modules. Pseudo-injective modules are dual to pseudo-projective modules. We study their properties and endomorphism rings, and obtain some properties of the Jacobson radical of such rings. 展开更多
关键词 pseudo-injective principally pseudo-injective idempotent principal self-generator endomorphism ring jacobson radical
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The Frattini Subalgebra of n-Lie Algebras 被引量:10
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作者 Rui Pu BAI Liang Yun CHEN Dao Ji MENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第5期847-856,共10页
In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacob... In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacobson radical are studied. Moreover, we also study them when an n-Lie algebra is strong semi-simple, k-solvable and nilpotent. 展开更多
关键词 n-Lie algebra the Frattini algebra jacobson radical
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Some Subsystems of a Lie Triple System Closely Related to Its Frattini Subsystem 被引量:2
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作者 Liangyun CHEN Dong LIU Xiaoning XU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2013年第5期791-800,共10页
The main purpose of the present paper is to give some properties of the Jacobson radical, the Frattini subsystem and c-ideals of a Lie triple system. Some further results concerning the Frattini subsystems of nilpoten... The main purpose of the present paper is to give some properties of the Jacobson radical, the Frattini subsystem and c-ideals of a Lie triple system. Some further results concerning the Frattini subsystems of nilpotent and solvable Lie triple systems are obtained. Moreover, we develop inititally c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system. 展开更多
关键词 Frattini subsystem jacobson radical c-ideals SOLVABLE NILPOTENT
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About Operator Weighted Shift 被引量:1
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作者 Chun Lan JIANG Yong Fei JIN Zong Yao WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第8期1385-1390,共6页
Abstract Let H be a complex seperable Hilbert space and ^(Jt^) denote the collection of bounded linear operators on H. For an operator in L(H), rad{A}' denotes the Jacobson radical of the commutant of A. This pap... Abstract Let H be a complex seperable Hilbert space and ^(Jt^) denote the collection of bounded linear operators on H. For an operator in L(H), rad{A}' denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}'/rad{A}'. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative. 展开更多
关键词 Operator weighted shift Strongly irriducible operator SIMILARITY COMMUTANT jacobson radical
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On the Derivations of Semiprime Rings and Noncommutative Banach Algebras
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作者 Byungdo Kim 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2000年第1期21-28,共8页
Let A be a noncommutative Banach algebra.Suppose there exists a continuous linear Jordan derivation D:A→A such that [D(x),x]D(x)[D(x),x]∈ rad(A) for all x ∈ A.In this case, D(A)rad(A).
关键词 Prime and semiprilne rings DERIVATIONS Jordan derivations jacobson radical Banach algebras Spectral radius
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Skew Incidence Rings and the Isomorphism Problem
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作者 Érica Z.Fornaroli 《Algebra Colloquium》 SCIE CSCD 2022年第3期419-426,共8页
Let X be a finite partially ordered set,R an associative unital ring andσan endomorphism of R.We describe some properties of the skew incidence ring I(X,R,σ)such as invertible elements,idempotents,the Jacobson radic... Let X be a finite partially ordered set,R an associative unital ring andσan endomorphism of R.We describe some properties of the skew incidence ring I(X,R,σ)such as invertible elements,idempotents,the Jacobson radical and the center.Moreover,if two skew incidence rings I(X,R,σ)and I(Y,S,τ)are isomorphic and the only idempotents of R and S are the trivial ones,we show that the partially ordered sets X and Y are isomorphic. 展开更多
关键词 units IDEMPOTENTS jacobson radical CENTER ISOMORPHISMS
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Noncommutative Versions of the Singer-Wermer Conjecture with Linear Left θ-derivations
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作者 Yong Soo JUNG Kyoo Hong PARK 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第11期1891-1900,共10页
The noncommutative Singer-Wermer conjecture states that every linear (possibly unbounded) derivation on a (possibly noncommutative) Banach algebra maps into its Jacobson radical. This conjecture is still an open q... The noncommutative Singer-Wermer conjecture states that every linear (possibly unbounded) derivation on a (possibly noncommutative) Banach algebra maps into its Jacobson radical. This conjecture is still an open question for more than thirty years. In this paper we approach this question via linear left θ-derivations. 展开更多
关键词 linear left θ-derivation linear θ-derivation jacobson radical nil radical
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The Necessary and Sufficient Condition for Strong Irreducibility of Cowen-Douglas Operators
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作者 HE Hua ZHU Guang Hui 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第3期666-670,共5页
In this note, we show that a Cowen-Douglas operator is strongly irreducible if and only if its commutant algebra rood its Jocobson radical is isomorphic to a closed subalgebra of H^∞ (D), where D is the open unit d... In this note, we show that a Cowen-Douglas operator is strongly irreducible if and only if its commutant algebra rood its Jocobson radical is isomorphic to a closed subalgebra of H^∞ (D), where D is the open unit disk, and H^∞(D) denotes the collection of bounded holomorphic functions on D. 展开更多
关键词 strongly irreducible Cowen-Douglas operator commutant algebra jacobson radical
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