S-Zip模

S-Zip Modules

引进S-zip模的概念。设R是一个具有单位元的任意环，M是一个右R-模，S=EndR（M）。称一个右R-模M是S-zip模，如果对于M的任一非空子集X，由X在S中的左零化子ls（X）=0可以推出存在一个有限子集Y∈X，使得ls（Y）=0。给出了S-zip模的一些刻画，讨论了S-zip模与相关模之间的关系，并且将zip环的一些已知结论拓广到S-zip模上。

We introduce in this paper the notion of S-zip modules. Let R be an arbitrary ring with identity and MR be a right R-module with S = EndR（M）. A module MR is called S-zip provided that if the left annihilator ls（X） of a subset X ≠0 of MR in S is zero, ls（Y）=0 for a finite subset Y∈X. We give several characterizations of S-zip modules and discuss the connections between S-zip modules and related modules, extending several results known for zip rings to S-zip modules.