1) Semisimple ring
半单环
1.
N-semisimple rings,Noether N-semisimple rings and some special rings;
N-半单环、Noether N-半单环和几类特殊环
2.
Left V-rings,semisimple rings,QF-rings,et al.
用FCG内射模刻画了V环、半单环、QF环等特殊环。
3.
Some characterizations of cofinitely related modules are given,conoetherian rings and V rings are characterized by cofinitely related modules,some conditions under which coregular rings are V rings are given,a condition under which left hereditary rings are semisimple rings is given too.
给出了有限余相关模的刻画 ,用有限余相关模刻画了余 Noether环和 V-环 ,给出了余正则环为 V-环的条件和遗传环为半单环的一个条件 。
2) semisimple rings
半单环
1.
2)Let R be kothe-semisimple rings,for any x,y∈R,there exist integers m=m(x,y)>1,n=n(x,y)>1, such that (x~my)~n-yx~m∈Z(R),then R is commutative.
2)设R为kothe半单环,若对R中任意元x,y,存在整数m=m(y)>1,n=n(x,y)>1,使得(xmy)n-yxm∈Z(R)则R为交换环。
2.
Furdermore,we define two kinds of special rings: n-p-semisimple rings and Gp-semisimple rings.
由此构造了两种特殊的环:n-p-半单环与Gp-半单环,并用新引入的模对它们分别进行了刻化。
3.
Furthermore, we define a kind of new rings by means of them ,called N-semisimple rings.
本文引入了N-投射模、N-内射模的概念,由此构造了一种环,称为N-半单环,并且证明出NoetherN-半单环是介于半单环与左遗传环之间的一种环。
3) semi-simple ring
半单环
1.
And semi-simple rings,Noetherian,V-rings,semi-Artinian rings,semi-local rings are characterized by pseudo-injective modules.
研究了伪内射模的性质,用伪内射模刻画了半单环,Noether、V-环,半Artin环和半局部环,得到的主要结果为:(1)伪内射模的完全不变子模是伪内射模;(2)R是半单环当且仅当伪内射模与半单模一致当且仅当半本原模是伪内射模,且本质基座的模是伪内射模当且仅当基座为0的模是伪内射模,伪内射模的直和伪内射;(3)R半Artin环当且仅当基座为0的模伪内射;(4)R是半局部环当且仅当R为左良好环且半本原模是伪内射模。
4) semi-simple rings
半单环
1.
In this paper,authors discuss respectively the necessary and sufficient conditions for the non-comutative semi-local rings as semi-simple rings,commutative semi-local rings and indecomposable commutative semi-local rings aslocal ring.
本文给出了非交挽半局部环为半单环的一系列充要条件,同时还讨论了交换半局部环,持别是不可分的交换半局部环为局部环的充要条件。
5) Jacobson semisimple semiring
Jacobson半单半环
6) simple semiring
单半环
补充资料：半单环
半单环
semi-ample ring
半单环[脚‘一滋田户d硬弓;助Jl”lpoc功“““城。1 根为零的环R.更确切地说，如果r是某种根(见环与代数的根(正山司ofnn乡anda」9 ebn玲))，环R称为;半单的(卜~一s如p卜)，是指r(R)“O通常人们将结合半单环理解为经共牛早环、。。~。一仁，漏司户6n。、.月.A.cxOP朋K邹撰冯绪宁译
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条