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

作　　者：班秀和 BAN Xiuhe(School of Mathematics and Statistics,Nanning Normal University,Nanning 530299,China)

机构地区：[1]南宁师范大学数学与统计学院

出　　处：《湖北民族学院学报（自然科学版）》2019年第4期403-406,共4页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(1166010212);广西自然科学基金重点项目(604167639055);广西硕士研究生创新项目(YCSW2018181)

摘　　要：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.

关 键 词：FS-环 FS-模 投射模 SF-环 PS-环 多项式模 

分 类 号：O153.3[理学—数学]