单投射半模的性质  

Properties of the simple-projective semimodules

作　　者：黄艳[1] 王颂生[1] 李娟[1] 邹雅文 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《西安工程大学学报》2017年第2期283-288,共6页Journal of Xi’an Polytechnic University

基　　金：江西省自然科学基金资助项目(11261021)

摘　　要：在投射半模的基础上引进单投射半模和单内射半模的概念,分析单投射半模p与Hom(p,-)函子、单投射半模_AP_i与直和项Pi的关系等,证明若投射半模M的商半模是内射半模,则M的任意单子半模必为M-单投射半模;进一步给出M-单投射半模与M k-投射半模的等价条件;证明相对于单投射半模的Schanuel引理.On the basis of projective semimodules, the concepts of the simple-projective semimodules and simple-injective semimodules are introduced.Some properties of the simple-projective semimodules are explored, for example, the relationship between the simple-projective semimodule p and Horn（p,-）, the relationship between the simple-projective semimodule GAPI and the direct sum item Pi. It is proved that if a factor semimodule of a projective semimodule M is an injective semimodule, then any subsemimodules of M is Msimple-projective semimodule. Moreover the equivalent conditions of the M-simple-projective semimodules and M k-projective semimodules are given. Last, Schanuel lemma of relatively simple-projective semimodules is proved.

关 键 词：单投射半模 因子定理 单子半模 Schanuel引理 完全强半模 

分 类 号：O153.3[理学—数学]