S-可除模及S-Dedekind环  

S-divisible Modules and S-Dedekind Rings

作　　者：高玉兵 王芳贵[1] 熊涛[1] GAO Yubing WANG Fanggui XIONG Tao(College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan)

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2016年第6期783-789,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11171240);教育部博士点专项科研基金(20125134110002)

摘　　要：设R是任何环,M是R-模.S是包含在R的中心内的非零因子乘法封闭集,对任意的非零因子u∈S,Ext1R(R/Ru,M)=0,则称M是S-可除模;若对任何S-正则左理想I,Ext1R(R/I,E)=0,则称E是S-正则内射模.环R称为S-Noether环,是指R的S-正则左理想是有限生成的.交换环R称为S-Dedekind环,是指R的任何S-正则理想是可逆理想.讨论S-Noether环的基本性质,并用S-可除模来刻画SDedekind环,证明R是S-Dedekind环当且仅当S-可除模是S-正则内射模.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 

分 类 号：O154[理学—数学]