As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelope...As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .展开更多
In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applicati...In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given.展开更多
In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, poly...In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.展开更多
Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr（a） = Ra＋Xa. We extend this notion to modules. A right R-module M with S = End（MR） is called quasi AP-...Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr（a） = Ra＋Xa. We extend this notion to modules. A right R-module M with S = End（MR） is called quasi AP-injective if, for any s∈S, there exists a left ideal Xs of S such that ls（Ker（s）） = Ss＋Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou.展开更多
Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module...Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.展开更多
In this article, we introduce and study the concept of n-Gorenstein injective （resp., n-Gorenstein flat） modules as a nontrivial generalization of Gorenstein injective （resp., Gorenstein flat） modules. We invest...In this article, we introduce and study the concept of n-Gorenstein injective （resp., n-Gorenstein flat） modules as a nontrivial generalization of Gorenstein injective （resp., Gorenstein flat） modules. We investigate the properties of these modules in various ways. For example, we show that the class of n-Gorenstein injective （resp., n -Gorenstein flat） modules is closed under direct sums and direct products for n ≥ 2. To this end, we first introduce and study the notions of n-injective modules and n-flat modules.展开更多
The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo...The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.展开更多
We introduce and investigate the concept of s-injective modules and strongly s-injective modules. New characterizations of SI-rings, GV-rings and pseudo-Frobenius rings are given in terms of s-injectivity of their mod...We introduce and investigate the concept of s-injective modules and strongly s-injective modules. New characterizations of SI-rings, GV-rings and pseudo-Frobenius rings are given in terms of s-injectivity of their modules.展开更多
A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper...A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper, PS-coherent rings as a generalization of P-coherent rings and J-coherent rings. To characterize PS-coherent rings, we first introduce PS-injective and PS-flat modules, and discuss the relation between them over some spacial rings. Some properties of left PS-coherent rings are also studied.展开更多
Let R be a ring. A right R-module M with S = End（MR） is called a quasi AP-injective module, if, for any s C S, there exists a left ideal Xs of S such that ls（ker s） = Ss＋Xs. Let M be a quasi AP-injective module w...Let R be a ring. A right R-module M with S = End（MR） is called a quasi AP-injective module, if, for any s C S, there exists a left ideal Xs of S such that ls（ker s） = Ss＋Xs. Let M be a quasi AP-injective module which is a self-generator. We show that for such a module, if S is semiprime, then every maximal kernel of S is a direct summand of M. Furthermore, if ker（a1） lohtain in ker（a2a1） lohtain in ker（a3a2a1） lohtain in... satisfy the ascending conditions for any sequence al, a2, a3,… ∈ S, then S is right perfect. In this paper, we give a series of results which extend and generalize results on AP-injective rings.展开更多
To overcome hole-injection limitation of p^＋-n emitter junction in 4H-SiC light triggered thyristor, a novel high- voltage 4H-SiC light triggered thyristor with double-deck thin n-base structure is proposed and demon...To overcome hole-injection limitation of p^＋-n emitter junction in 4H-SiC light triggered thyristor, a novel high- voltage 4H-SiC light triggered thyristor with double-deck thin n-base structure is proposed and demonstrated by two- dimensional numerical simulations. In this new structure, the conventional thin n-base is split to double-deck. The hole- injection of p^＋-n emitter junction is modulated by modulating the doping concentration and thickness of upper-deck thin n- base. With double-deck thin n-base, the current gain coefficient of the top pnp transistor in 4H-SiC light triggered thyristor is enhanced. As a result, the triggering light intensity and the turn-on delay time of 4H-SiC light triggered thyristor are both reduced. The simulation results show that the proposed 10-kV 4H-SiC light triggered thyristor is able to be triggered on by 500-mW/cm^2 ultraviolet light pulse. Meanwhile, the turn-on delay time of the proposed thyristor is reduced to 337 ns.展开更多
Electroabsorption modulators combining Franz-Keldysh effect and quantum confined Stark effect have been mono-lithically integrated with tunnel-injection quantum-well distributed feedback lasers using a quantum well in...Electroabsorption modulators combining Franz-Keldysh effect and quantum confined Stark effect have been mono-lithically integrated with tunnel-injection quantum-well distributed feedback lasers using a quantum well intermixing method. Superior characteristics such as extinction ratio and temperature insensitivity have been demonstrated at wide temperature ranges.展开更多
An injection-seeded single-frequency Q-switched Nd：YAG laser is accomplished by using a phase modulated rampfire technique. A RbTiOPO4（RTP） electro-optic crystal is selected for effective optical path length modula...An injection-seeded single-frequency Q-switched Nd：YAG laser is accomplished by using a phase modulated rampfire technique. A RbTiOPO4（RTP） electro-optic crystal is selected for effective optical path length modulation of the slave self-filtering unstable resonator. This single-frequency laser is capable of producing 50 m J pulse energy at 1 Hz repetition rate with a pulse width of 16 ns. The standard deviation of laser pulse intensity for consecutive 100 shots from the mean pulse intensity is less than 1.05%. A spectral linewidth of less than 0.5 pm with a frequency jitter of about 14 fm over30 min is obtained.展开更多
For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and duali...For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.展开更多
In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. W...In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. We show that IFP-fd（M） = IFP-id（M＋） and IFP-fd（M＋）=IFP-id（M） for any R-module M over any ring R. Let ：Z-In （resp., ＂Zgv,~） he the class of all left （resp., right） R-modules of IFP-injective （resp., IFP-flat） dimension at most n. We prove that every right R-module has an IFn- preenvelope, （IFn,IF⊥n） is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id（RR） 〈 n, （IIn,II⊥n） is a perfect cotorsion theory. This generalizes and improves the earlier work （J. Algebra 242 （2001）, 447-459）. Finally, some applications are given.展开更多
In the Paper,the author introduces an embedded design verification test based on specific chips to solve the technical problems of microwave circuit test and fault diagnosis.The author explains embedded design of micr...In the Paper,the author introduces an embedded design verification test based on specific chips to solve the technical problems of microwave circuit test and fault diagnosis.The author explains embedded design of microwave circuit modules and approach of hardware design and software design,and finally verifies the embedded design of microwave circuit modules based on specific chips.展开更多
It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close conne...It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close connections among injective cogenerators,cotilting modules and cosilting modules from the viewpoint of morphism categories.Some applications are also given.展开更多
文摘As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .
基金Supported by the National Natural Science Foundation of China（11361051） Supported by the Program for New Century Excellent the Talents in University（NCET-13-0957）
文摘In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given.
基金Supported by the NNSF of China(10901129)Supported by the SRFDP(20096203120001)
文摘In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.
文摘Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr（a） = Ra＋Xa. We extend this notion to modules. A right R-module M with S = End（MR） is called quasi AP-injective if, for any s∈S, there exists a left ideal Xs of S such that ls（Ker（s）） = Ss＋Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou.
基金This research is in part supported by a grant from IPM.
文摘Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.
基金The NSF(11501451)of Chinathe Fundamental Research Funds(31920150038)for the Central Universities and XBMUYJRC(201406)
文摘In this article, we introduce and study the concept of n-Gorenstein injective （resp., n-Gorenstein flat） modules as a nontrivial generalization of Gorenstein injective （resp., Gorenstein flat） modules. We investigate the properties of these modules in various ways. For example, we show that the class of n-Gorenstein injective （resp., n -Gorenstein flat） modules is closed under direct sums and direct products for n ≥ 2. To this end, we first introduce and study the notions of n-injective modules and n-flat modules.
基金Supported by the Ph.D.Programs Foundation of Ministry of Education of China(200803570003)
文摘The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.
文摘We introduce and investigate the concept of s-injective modules and strongly s-injective modules. New characterizations of SI-rings, GV-rings and pseudo-Frobenius rings are given in terms of s-injectivity of their modules.
文摘A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper, PS-coherent rings as a generalization of P-coherent rings and J-coherent rings. To characterize PS-coherent rings, we first introduce PS-injective and PS-flat modules, and discuss the relation between them over some spacial rings. Some properties of left PS-coherent rings are also studied.
文摘Let R be a ring. A right R-module M with S = End（MR） is called a quasi AP-injective module, if, for any s C S, there exists a left ideal Xs of S such that ls（ker s） = Ss＋Xs. Let M be a quasi AP-injective module which is a self-generator. We show that for such a module, if S is semiprime, then every maximal kernel of S is a direct summand of M. Furthermore, if ker（a1） lohtain in ker（a2a1） lohtain in ker（a3a2a1） lohtain in... satisfy the ascending conditions for any sequence al, a2, a3,… ∈ S, then S is right perfect. In this paper, we give a series of results which extend and generalize results on AP-injective rings.
基金supported by the National Natural Science Foundation of China(Grant No.51677149)
文摘To overcome hole-injection limitation of p^＋-n emitter junction in 4H-SiC light triggered thyristor, a novel high- voltage 4H-SiC light triggered thyristor with double-deck thin n-base structure is proposed and demonstrated by two- dimensional numerical simulations. In this new structure, the conventional thin n-base is split to double-deck. The hole- injection of p^＋-n emitter junction is modulated by modulating the doping concentration and thickness of upper-deck thin n- base. With double-deck thin n-base, the current gain coefficient of the top pnp transistor in 4H-SiC light triggered thyristor is enhanced. As a result, the triggering light intensity and the turn-on delay time of 4H-SiC light triggered thyristor are both reduced. The simulation results show that the proposed 10-kV 4H-SiC light triggered thyristor is able to be triggered on by 500-mW/cm^2 ultraviolet light pulse. Meanwhile, the turn-on delay time of the proposed thyristor is reduced to 337 ns.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60736036,60706009,60777021 and 60702006)the National Basic Research Program of China (Grant Nos. 2006CB604901 and 2006CB604902)the National High Technology Research and Development Program of China (Grant Nos. 2007AA03Z419,2007AA03Z417 and 2009AA03Z442)
文摘Electroabsorption modulators combining Franz-Keldysh effect and quantum confined Stark effect have been mono-lithically integrated with tunnel-injection quantum-well distributed feedback lasers using a quantum well intermixing method. Superior characteristics such as extinction ratio and temperature insensitivity have been demonstrated at wide temperature ranges.
基金Project supported by the National Key Research and Development Program of China(Grant Nos.2017YFB1104500 and 2016YFB0701000)
文摘An injection-seeded single-frequency Q-switched Nd：YAG laser is accomplished by using a phase modulated rampfire technique. A RbTiOPO4（RTP） electro-optic crystal is selected for effective optical path length modulation of the slave self-filtering unstable resonator. This single-frequency laser is capable of producing 50 m J pulse energy at 1 Hz repetition rate with a pulse width of 16 ns. The standard deviation of laser pulse intensity for consecutive 100 shots from the mean pulse intensity is less than 1.05%. A spectral linewidth of less than 0.5 pm with a frequency jitter of about 14 fm over30 min is obtained.
文摘For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.
基金supported by National Natural Science Foundation of China(10961021,11001222)
文摘In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. We show that IFP-fd（M） = IFP-id（M＋） and IFP-fd（M＋）=IFP-id（M） for any R-module M over any ring R. Let ：Z-In （resp., ＂Zgv,~） he the class of all left （resp., right） R-modules of IFP-injective （resp., IFP-flat） dimension at most n. We prove that every right R-module has an IFn- preenvelope, （IFn,IF⊥n） is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id（RR） 〈 n, （IIn,II⊥n） is a perfect cotorsion theory. This generalizes and improves the earlier work （J. Algebra 242 （2001）, 447-459）. Finally, some applications are given.
文摘In the Paper,the author introduces an embedded design verification test based on specific chips to solve the technical problems of microwave circuit test and fault diagnosis.The author explains embedded design of microwave circuit modules and approach of hardware design and software design,and finally verifies the embedded design of microwave circuit modules based on specific chips.
基金Supported by NSFC(Grant Nos.12171230,12271249)NSF of Jiangsu Province of China(Grant No.BK20211358)。
文摘It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close connections among injective cogenerators,cotilting modules and cosilting modules from the viewpoint of morphism categories.Some applications are also given.
