Morita Context环的幂零性

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.     

Morita Context环的若干性质

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.     

具有一对零态射的Morita Context 环(Ⅱ)

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.     

具有一对零态射的Morita Context环(II)

设$(A,B,V,W,\psi,\phi)$是一个Morita Context,具有一对零态射$\psi=0$, $\phi=0$, $C =\left ( \begin{array} {cc}A & V \\W & B \end{array}\right)$是对应的Morita Context环.本文给出了$C$与$A,B,V,W$之间关于环的$\pi$-正则性、semiclean性、Mophic性和环的Exchgange性、Potent性、GM性的关系.     

Morita Context的右正规性

本文讨论了Muller提出的第3个公正问题，证明了当PR是忠帝的拟投射生成元，PT＝P，且T作为右R－模有限生成时，PR导出的Morita Context一定是右正规性的，这里T为P在R中的变理想。     

正规幂环和一致幂环

文[1]首次提出了HX环（幂环）的概念,文[2]探索了幂环的性质和结构,本文类似于幂群的研究,提出了正规幂环和一致幂环的概念,研究了它们的结构和它们之间的关系,对它们进行了分类,并讨论了它们的交与和,从而构造了它们的子环链和理想链。     

素GPI-环的幂零多项式

R是素 GPI-环 ,若多项式 f (x1,… ,xd)在 R上是幂零的 ,则或 f (x1,… ,xd)是 R的恒等式 ,或 R是有限域上的有限矩阵环 .     

一般环之因子幂零理想

本文称环Ω的左(右)理想A为因子幂零的,如果对于任意元素r∈Ω,均有正整数m=m(r),使得A^mr={0}.称Ω的一个左理想L为关于元素b∈Ω的左因子,如果Lb≠{0}.定理4 设R是环Ω的因子幂零右理想,那么R+ΩR是Ω的一个因子幂零理想.定理7 设Ω具有局部左因子极小条件,那么Ω的任意诣零左理想必是因子幂零左理想.本文指出因子幂零性是介于幂零性与诣零性之间的一种性质,更接近幂零性。     

模消去的Morita Contexts

证明了置换环上n-稳定秩条件关于Morita Context是遗传的;进一步把该结果推广到了强可分环,从而提供了新的具有模消去的置换环。     

MORITA THEORY FOR ASSOCIATIVE RINGS

In this paper we develop a Morita theory for associative rings without identity using the categories CMod-R of modules M such that M ? Hom(R,M) and DMod-R of modules M such that M ? R ? M. This extends the main results of Morita theory to a wide class of rings, that properly includes the idempotent rings.     

EXCHANGE MORITA RINGS

In this paper we characterize the largest exchange ideal of a ring R as the set of those elements x ∈ R such that the local ring of R at x is an exchange ring. We use this result to prove that if R and S are two rings for which there is a quasi-acceptable Morita context, then R is an exchange ring if and only if S is an exchange ring, extending an analogue result given previously by Ara and the second and third authors for idempotent rings. We introduce the notion of exchange associative pair and obtain some results connecting the exchange property and the possibility of lifting idempotents modulo left ideals. In particular we obtain that in any exchange ring, orthogonal von Neumann regular elements can be lifted modulo any one-sided ideal.     

Hopf代数胚上的Smash积的Maschke型定理和Morita关系

本文研究了Hopf代数胚上的Smash积代数.利用Hopf代数胚的积分理论,获得了Hopf代数胚上的Smash的Maschke型定理并构造了一个Morita关系,推广了Cohen和Fishman在文献[1]中的相应结果.作为应用,获得了Hopf代数胚上的余模代数的Maschke型定理.     

TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS

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.     

ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS

Abstract

If a sum of univariate polynomials is zero, then there are restrictions on the multiplicities of zeros of the polynomials.     

MORITA NEAR-RINGS

Abstract

We define a morita context for near-rings and subsequently a morita near-ring. Any near-ring can be considered as a morita context for near-rings, and the corresponding morita near-ring is just the 2 x 2 matrix near-ring over the near-ring. We also determine the relationships between the ideals of a morita context and the ideals of a morita near-ring.