关于u-上临界模与u-半临界模

On u-cocritical module and u-semicritical module

引进了u-上临界模与u-半临界模.一个模M称为u-上临界的,如果M是u-缺挠模,并且M的每一个商模(不等于M)都是τu-挠模.一个模M称为u-半临界的,如果存在M的有限子模族{M1,M2,…,Mn}使得∩in=1Mi=0,M/Mi为u-上临界模.讨论了u-上临界模的基本性质,比较u-上临界模与u-半临界模的关系,并在一定条件下将它们与遗传挠理论统一起来.

This paper employ u-cocritical module and u-semicritical module.A module M is called u-cocritical if M is u-torsionless and if every proper factor module of M is τu-torsion.A module M is called u-semicritical if there exists finite submodule variety {M1,M2,…,Mn）of M,such that ∩n i=1Mi=0,and M/Mi is u-cocritical.In this paper,we deal with the basis properties of u-cocritical module and u-semicritical module.Moreover,under some given conditions,we integrate them with hereditary torsion theory.