四川师范大学学报（自然科学版）2016，Vol.39Issue(6)：784-789,6.DOI:10.3969/j.issn.1001-8395.2016.06.001
S-可除模及S-Dedekind环
S-divisible Modules and S-Dedekind Rings
摘要
Abstract
Let R be a ring and M be a R-module.Let S denote the regular multiplicative closed set of the center in R.If Ext(R/Ru,M)=0,for any regular element u∈S,then M is called an S-divisible modules.A left R-module E is called an S-regular injective if Ext(R/I,E)=0 for any S-regular left ideal I.R is called an S-Notherian rings if every S-regular left ideal in R is finitely generated.A commutative ring is called an S-Dedekind ring if every S-regular ideal in R is invertible.In this paper,we discuss the basic properties of S-Noetherian rings.With S-divisible modules characterized S-Dedekind rings,it is also shown that R is an S-Dedekind rings if and only if S-divisible modules are S-regular injective modules.关键词
S-正则理想/S-可除模/S-正则内射模/S-Noether环/S-Dedekind环Key words
S-regular ideals/S-divisible modules/S-regular injective modules/S-Noetherian rings/S-Dedekind rings分类
数理科学引用本文复制引用
高玉兵,王芳贵,熊涛..S-可除模及S-Dedekind环[J].四川师范大学学报（自然科学版）,2016,39(6):784-789,6.基金项目
国家自然科学基金(11171240)和教育部博士点专项科研基金(20125134110002) （11171240）
