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1.
The notion of the xst-rings was introduced by Garcfa and Marfn [5] in 1999.In this paper,we cousider Morita context,Morita-like equivalence and the exchange property for the xst-rings.The results of the first Morita theorem are generalized to the xst-rings.So we obtain an important Morita-like equivalence of the xst-rings,from which,as an immediate consequence,we deduce the main result of Xu-Shum-Turner [4] and the standard Morita equivalence,A-Mn(A),for a unital ring A.Moreover,we describe the properties of those well-known intermediate matrix rings,and show that the exchange property for a unital ring A coincides with the one for any Mn(A) as well as any intermediate matrix ring sitting between FM1(A) and FCг(A),which is an extension of a well-known result obtained by Nicholson[7].  相似文献   

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We characterize the lattice of all ideals of a Morita ring (semigroup) when the corresponding pair of rings (semigroups) in the Morita context are Morita equivalent s-unital (like-unitv) rings (semigroups).  相似文献   

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分次Morita对偶,Morita对偶与Smash积   总被引:1,自引:0,他引:1  
张圣贵 《数学学报》1994,37(6):756-761
设C和r都是群,是G-型分次环,是Γ-型分次环.是双分次模,R#G是R的Smash积,A#Γ是A的Smash积。令W=(_gU_(σ-1))_(g,σ)即(g,σ)位置取_gU_(σ-1)的元素的|G|×|Γ|矩阵的全体组成的集合,且每个矩阵的每行和每列的非零元只有有限个,按矩阵运算,W构成(R#6,A#Γ)双模。则_RU_A定义了一个分次Morita对偶当且仅当_(R#G)W_(A#Γ)定义了一个Morita对偶。  相似文献   

5.
朱彬  王尧 《数学研究》1997,30(2):188-192
设R是G-分次环,A是G-集,(H,B)的忠实子对象,本文讨论了分次模范畴(A,R)-gr与分次模范范畴(B,Rn)-gr等价的条件;给出了R#A是单环,R#G/H是素环的刻划,所得结果均推广了已有结论。  相似文献   

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本文讨论了群分次代数A与其SmashProductA#G的循环同调群之间的关系,并且在A分别是有限分次,强分次,以及非负分次的情形下得出一些刻划两者内在联系的结论。  相似文献   

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本文讨论了群分次代数A与其SmashProductA#G的循环同调群之间的关系,并且在A分别是有限分次,强分次,以及非负分次的情形下得出一些刻划两者内在联系的结论.  相似文献   

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Morita对偶和Smash积   总被引:1,自引:1,他引:0  
张圣贵 《数学学报》1991,34(4):561-565
设G是有限群,e为G的单位元,R=是有单位元的G-型分次环,T=R_e,R_U是极小内射余生成子.本文中,我们证明了R有左Morita对偶当且仅当Smash积R#G有左Morita对偶.设H是G的(正规)子群,若R有左Morita对偶,则R~((H))#H(R_((G/H))#(G/H))有左Morita对偶。当R是强分次环时,T有左Morita对偶当且仅当R有左Morita对偶当且仅当R#G有左Morita对偶.  相似文献   

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本文讨论了QuotientContextof Morita Context的一些性质,并在此基础上证明:如果DR是一个完备Gabriel拓扑,则一个(P,Q)的商(P,Q)作为R与S之间MC,它的商同构于(P,Q)的一个商。  相似文献   

10.
Morita Context环的若干性质   总被引:1,自引:1,他引:0  
研究由Morita Contexts所确定的环,讨论它的K-好环性质,弱Semicom-mutative性质,有许多单式正则元性质和广义稳定环性质等.  相似文献   

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设(A,B,V,W,(),[])是一个Morita Context,C=A VW B是对应的Morita Context环.用基本环论方法,给出了C与A,B,V,W之间关于环的诣零性,幂零性,局部幂零性,N—诣零性,P—性等性质的关系.  相似文献   

12.
Adriana Balan 《代数通讯》2013,41(4):1129-1150
If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we show that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A H . We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case.  相似文献   

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In this article we prove that the extended centroid of a nondegenerate Jordan system is isomorphic to the centroid (and to the center in the case of Jordan algebras) of its maximal Martindale-like system of quotients with respect to the filter of all essential ideals.  相似文献   

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