1) congruence-simple semiring
c-单半环
2) c-semiring
c-半环
1.
At last,we obtain the following three results:as the algebra of independent subsets of the ordered monoid(A~*,≤_h),the set H(A) of hypercodes on A forms a free incline;moreover,the subsets H_c(A) and H_(mic)(A) of H(A) can be constructed as a free c-semiring and a free mic-semiring,respectively.
作为序幺半群(A~*,≤_h)的无关子集的代数结构,A上的超码集H(A)形成自由坡,超码集的子集c-超码集H_c(A)构成自由c-半环,超码集的子集mic-超码集正H_(mic)(A)构成自由mic-半环。
3) Jacobson semisimple semiring
Jacobson半单半环
4) simple semiring
单半环
5) 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。
6) 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。
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