关于局部Artin模的一个定理  

A THEOREM ON LOCALLY ARTINIAN MODULES

作　　者：熊蕙萍[1] 

机构地区：[1]南昌大学数学与系统科学系

出　　处：《南昌大学学报（理科版）》1998年第3期195-199,共5页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学基金

摘　　要：证明了对于Ｒ－模Ｍ如下条件等价：（ⅰ）Ｍ是局部Ａｒｔｉｎ的；（ⅱ）σ〔Ｍ〕中每个循环模是一个自投射的Ｍ－单射模和一个有限上生成模的直和。如果Ｍ是循环自投射模的直和，那么（ⅰ），（ⅱ）等价于：（ⅲ）σ〔Ｍ〕中每个循环模是一个Ｍ－单射模和一个有限上生成模的直和。这使我们能够将Ｏｓｏｆｓｋｙ关于具有单位元的环的著名结果，推广到更加广泛的情形。In this paper,it is shown that for an R- module M the following are equivalent: \ \ (ⅰ)\ M is locally artinian; \ \ (ⅱ)\ every cyclic module in σ M is a direct sum of a self-projective M- injective module and a finitely cogenerated module. \ \ If M is a direct sum of cyclic self-projective modules then (ⅰ) and (ⅱ) are equivalent to: \ \ (ⅲ)\ every cyclic module in σ M is a direct sum of an M-injective module and a finitely cogenerated module. \ \ This enables us to extend a famous result of Osofsky's for rings with unit to the more general case.

关 键 词：自投射模 单射模 局部Artin模 直和 ARTIN模 

分 类 号：O153.3[理学—数学]