semisimple modules

In this paper,semirings,semimodules and congruence relations are defined,and following the correspondence between subsemimodules of semimodules and their congruence relations,strong semimodules and simple semimodules are induced.

提出半环、半模、余关系等概念,给出了半模的子半模关系之间的对应关系,并由余关系导出强半模和单半模的概念,得到半环和。

A necessary and sufficient condition for semi-sigleton module becomes self-reflective is givenin the paper,it is proved thus a semi-sigleton module can be decomposed finitely if andonly if it is isomorphic to a vector space of dimension n on a division ring.

本文给出了一个关于可有限分解的半单纯模为自反模的一个充分必要条件，从而证明了可有限分解的半单纯模为自反模当且仅当X同构于某个除环上的n维向量空间。