Semisimple linear transfor-mation

On cosemisimple Hopf algebras contains simple subcoalgebra of dimension p~2;

关于含p~2维单子余代数的余半单Hopf代数

After introducing some preliminaries and notations,the paper investigates semisimple Malcev algebras,giving some equivalent definitions and properties of semisimple Malcev algebras.

在列举了一些马力茨夫代数的基本知识之后,主要讨论了半单马力茨夫代数。

In this paper, we introduce the concepts of semisimple,totally semisimple S-sys-tems and M-projective S-system ,etc.

引进了半单、全半单Ｓ—系及Ｍ—投射Ｓ—系等概念，讨论了它们的一些性质，得到了一些重要的结果；并研究了所有全单Ｓ—系均Ｓ—投射的幺半群，推广了Ｊ。

2)let R be kthe-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。

The semisimplicity of pointed YD Lie algebras was characterized by means of Killing forms.

利用Killing型来判断点YD-李代数的半单性,得出了如下结论:如果有限维点YD-李代数L的Killing型是非退化的,那么L是半单的,并且L是它本身的所有极小YD-理想的直和;这些极小YD-理想所对应的Killing型两两正交。

By describing general superfluous convex l-subgroups in this paper, we prove the following results: If G is a normal-valued l-group, then (1)T= {x∈G|x<<u, u is a strong unit of G} ; (2) T = 0 iff G is l- isomorphic to a subdirect product of simple l-groups with semisimplicity.

证明了如下结果:如 果G是正规值l-群,则(1)T={x∈G|x<

In this paper we consider the semisimplicity of implicative BCK-alge-bras and obtain several equivalent conditions which an implicative BCK-algebra is semisimple.

本文考虑关联BCK－代数的半单性，得到这类代数为半单的若干等价条件。

In order to calculate efficiently the simplest normal form(SNF)of differential semi-simple systems without center manifold reduction,the relationship between the SNF and the original equations was deducted based on matrix representation method.

为了在不经中心流形降维的情况下高效计算半单系统的最简规范形,基于矩阵表示法研究了半单系统的最简规范形。

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。

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。

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。