设(A,B,V,W,ψ,φ)是一个Morita Context,具有一对零态射ψ=0,φ=0,C= (A V W B)是对应的Morita Context环.本文给出了C与A,B,V,W之间关于环的π-正则性、semiclean性、Mophic性和环的Exchgange性、Potent性、GM性的关系.
In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also a...In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also an exchange ring satisfying the comparability.This provides a new class of exchange rings satisfying the comparability.Furthermore,we investigate the s-comparability over exchange rings.This generalizes the corresponding results of Goodearl and Chen.展开更多
We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and...We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.展开更多
We obtaim a new substitution for modules over exchange rings satisfving related compara- bilitv. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class ...We obtaim a new substitution for modules over exchange rings satisfving related compara- bilitv. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class of exchange rings satisfying related comparability.展开更多
Development of high-performance hydroxide-conductive membranes is a focus research subject owing to promising applications in electrochemical reduction of CO_(2)(eCO_(2)RR).However,few satisfactory membranes have been...Development of high-performance hydroxide-conductive membranes is a focus research subject owing to promising applications in electrochemical reduction of CO_(2)(eCO_(2)RR).However,few satisfactory membranes have been developed to maximize the performance of CO_(2) electrolyzers,despite its role as the core in regulating ion transport and preventing product crossover or fuel loss.Herein,we report the synthesis of alkaline anion-exchange membranes fabricated by poly(vinyl-alcohol)(PVA)and poly[(3-methyl-1-vinylimidazoliummethylsulfate)-co-(1-vinylpyrrolidone)](PQ44)for use in CO_(2) electrolysis.Owing to the unique imidazolium ring structure coupled with a three-dimensional semiinterpenetrating porous internal architecture,the PVA/PQ44-OH-membranes provide a high hydroxide conductivity(21.47 mS cm^(-1)),preferable mechanical property and thermal stability.In particular,the eCO_(2)RR used PVA/PQ44-OH^(-) as electrolyte membrane realized a charming Faradaic efficiency(88%)and partial current density(29 mA cm^(-2))at0.96 VRHE and,delivered the excellent durability over 20 h electrolysis in 0.5 mol L^(-1) KHCO_(3) electrolyte.Notably,it can even enable an ultrahigh current density beyond 100 mA cm^(-2) at^(-1).11 VRHE when the electrolyte was KOH instead,and produced the FEHCOOof 85%at a low potential of0.81 VRHE,superior to both commercial alkaline A201 and acidic Nafion117 membrane.展开更多
Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U（R） such that 1R ± u ∈ U（R）, if and only if for any a ∈ R, there exists a u ∈ U（R） such that a ± u∈ U（R...Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U（R） such that 1R ± u ∈ U（R）, if and only if for any a ∈ R, there exists a u ∈ U（R） such that a ± u∈ U（R）. Phrthermore, we prove that, for any A ∈ Mn（R）（n ≥ 2）, there exists a U ∈ GLn（R） such that A ± U ∈ GLn（R）.展开更多
A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to...A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H（R） andT（R,a）. The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent： that is R is pseudo weakly clean; there is an integer n such thatR[x]/（x^n） is pseudo weakly clean; there is an integer n such that R[[x]]/（x^n） is pseudo weakly clean.展开更多
文摘设(A,B,V,W,ψ,φ)是一个Morita Context,具有一对零态射ψ=0,φ=0,C= (A V W B)是对应的Morita Context环.本文给出了C与A,B,V,W之间关于环的π-正则性、semiclean性、Mophic性和环的Exchgange性、Potent性、GM性的关系.
基金This work is supported by the National Natural Science Foundation of China (Grant No.19801012)the Ministry of Education of China.
文摘In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also an exchange ring satisfying the comparability.This provides a new class of exchange rings satisfying the comparability.Furthermore,we investigate the s-comparability over exchange rings.This generalizes the corresponding results of Goodearl and Chen.
基金supported by the guidance project of scientific research plan of Educational Adminstration of Hubei Province,China(B2016162)the plan of science and technology innovation team of excellent young and middle-age of Hubei province(T201731)
文摘We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.
基金This work is supported by the National Natural Science Foundation of China (Grant No. 19801012. 19531020).
文摘We obtaim a new substitution for modules over exchange rings satisfving related compara- bilitv. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class of exchange rings satisfying related comparability.
基金support from the“Scientific and Technical Innovation Action Plan”Basic Research Field of Shanghai Science and Technology Committee (19JC1410500)the National Natural Science Foundation of China (21972017).
文摘Development of high-performance hydroxide-conductive membranes is a focus research subject owing to promising applications in electrochemical reduction of CO_(2)(eCO_(2)RR).However,few satisfactory membranes have been developed to maximize the performance of CO_(2) electrolyzers,despite its role as the core in regulating ion transport and preventing product crossover or fuel loss.Herein,we report the synthesis of alkaline anion-exchange membranes fabricated by poly(vinyl-alcohol)(PVA)and poly[(3-methyl-1-vinylimidazoliummethylsulfate)-co-(1-vinylpyrrolidone)](PQ44)for use in CO_(2) electrolysis.Owing to the unique imidazolium ring structure coupled with a three-dimensional semiinterpenetrating porous internal architecture,the PVA/PQ44-OH-membranes provide a high hydroxide conductivity(21.47 mS cm^(-1)),preferable mechanical property and thermal stability.In particular,the eCO_(2)RR used PVA/PQ44-OH^(-) as electrolyte membrane realized a charming Faradaic efficiency(88%)and partial current density(29 mA cm^(-2))at0.96 VRHE and,delivered the excellent durability over 20 h electrolysis in 0.5 mol L^(-1) KHCO_(3) electrolyte.Notably,it can even enable an ultrahigh current density beyond 100 mA cm^(-2) at^(-1).11 VRHE when the electrolyte was KOH instead,and produced the FEHCOOof 85%at a low potential of0.81 VRHE,superior to both commercial alkaline A201 and acidic Nafion117 membrane.
基金Supported by Natural Science Foundation of Hunan Province(04JJ40003)
文摘Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U（R） such that 1R ± u ∈ U（R）, if and only if for any a ∈ R, there exists a u ∈ U（R） such that a ± u∈ U（R）. Phrthermore, we prove that, for any A ∈ Mn（R）（n ≥ 2）, there exists a U ∈ GLn（R） such that A ± U ∈ GLn（R）.
文摘A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H（R） andT（R,a）. The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent： that is R is pseudo weakly clean; there is an integer n such thatR[x]/（x^n） is pseudo weakly clean; there is an integer n such that R[[x]]/（x^n） is pseudo weakly clean.
