几类w-模的Krull-Remak-Schmidt定理  

The Krull-Remak-Schmidt Theorem on Several Classes of w-Modules

作　　者：张俊[1,2] 王芳贵[1] 

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 [2]四川师范大学外国语学院,四川成都610101

出　　处：《四川师范大学学报（自然科学版）》2011年第5期601-604,共4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(20060636001)资助项目

摘　　要：研究了具有w-子模链条件的模上同态,推广了Schur引理,证明了在Krull-Remak-Schmidt定理的观点下,几类w-模可以唯一分解为自同态环是局部环的不可分解子模的直和.In this paper,we investigate the homomorphisms on several classes of w-modules which satisfy ascending and descending chain conditions on w-submodules and generalize the Schur lemma.Moreover,we discuss the uniqueness problem of direct decomposition of modules in view point of the Krull-Remak-Schmidt theorem and prove that several classes of w-modules can be decomposed into a direct sum of directly indecomposable submodules with local endomorphism rings.

关 键 词：w-模 同态 Krull-Remak-Schmidt定理 分解 

分 类 号：O154[理学—数学]