直内射模的研究  

Research on Direct Injective Modules

作　　者：张伟民[1] 

机构地区：[1]北方交通大学数学系

出　　处：《北方交通大学学报》1995年第4期440-442,共3页Journal of Northern Jiaotong University

摘　　要：在Ｄｉｒｅｃｔｉｎｊｅｃｔｉｖｅｍｏｄｕｌｅｓ的基础上进一步讨论了直内射模的性质，得到了直内射模的几个等价条件和性质：若是直内射模，则Ｍａ是直内射模；模Ｍ为直内射模对每个单同态ｆ：Ｎ→Ａ（Ｎ为Ｍ的直和顶，Ａ为Ｍ的包含Ｎ的任意子模）有Ｈｏｍ（ｆ，Ｍ）：Ｈｏｍ（Ａ，Ｍ）→Ｈｏｍ（Ｎ，Ｍ）是满同态。In this paper, with a further discussion on the basis of reference, several equivalent conditions and properties of direct injective modules are obtained, i. e., a direct summand of direct injective module is a direct injective modules; module M is a direct injective module for each monomorphism f: N→A(N is a direct summand of M,A is any submodule of M and),and the mapping Hom(f, M):Hom(A,M)→Hom( N,M) surjective; if is a direct injective module, then Mα so is Mα.

关 键 词：模 内射模 直内射模 模论 

分 类 号：O153.3[理学—数学]