1) N-semisimple rings
N-半单环
1.
The concept of N-left hereditary rings is introduced,the equivalence theorem of Noether N-left hereditary rings is given,and coherent rings,QF rings and N-semisimple rings via Noether N-left hereditary rings are characterized.
引入了N-左遗传环的概念,给出了NoetherN-左遗传环的等价命题,并利用NoetherN-左遗传环对凝聚环和N-半单环进行刻画。
2.
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。
2) n-p-semisimple rings
n-p-半单环
1.
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) Noether N-semisimple ring
Noether N-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
4) Jacobson semisimple semiring
Jacobson半单半环
5) simple semiring
单半环
6) semisimple ring
半单纯环
1.
2)let R be kthe-semisimple rings,for any x,y∈R,there exist integers m=m(x,y)≥n=n(x,y)≥0,fx,y(t)∈t2Z[t],such that fx,y(xmy)-yxn∈Z(R) or fx,y(yxm)-yxn∈Z(R),then R is commutative.
2)设R为k the半单纯环,若对R中任意x,y,存在整数m=m(x,y)≥n=n(x,y)≥0,多项式fx,y(t)∈t2Z[t]使得fx,y(xmy)-yxn∈Z(R)或fx,y(yxm)-yxn∈Z(R),则R为交换环。
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
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参考词条