FS-环与FS-模的特征及FS-环与SF-环、PS-环的关系

Characterizations of FS-rings and FS-modules and Relations between FS-rings and SF-rings,PS-rings

对FS-环、FS-模进行了研究,给出了FS-环、FS-模的若干性质,指出了FS-环是SF-环的实质性推广,得到了FS-环是SF-环、FS-环是PS-环以及单侧FS-环是双侧FS-环的几个条件,还给出了多项式环上的多项式模是FS-模的一个充分条件.

In this paper,we study FS-rings and FS-modules,and some properties of FS-rings and FS-modules are given.We get an example which shows that an FS-ring need not be an SF-ring.Several conditions are given that an FS-ring is an SF-ring,an FS-ring is a PS-ring,a left FS-ring is a right FS-ring.And one sufficient condition that a polynomial module over a polynomial ring is an FS-module is given.