弱单投射半模  

Weak simple projective semimodules

作　　者：曾慧平[1] 张传美[1] 刘浩广[1] ZENG Huiping;ZHANG Chuanmei;LIU Haoguang(Science and Technology College,Nanchang Hangkong University,Nanchang 330034,China)

机构地区：[1]南昌航空大学科技学院

出　　处：《安徽大学学报（自然科学版）》2019年第5期17-21,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11561032,11801239);江西省教育厅科学技术研究青年项目(GJJ171520)

摘　　要：给出弱单投射半模的定义及弱单投射半模的等价刻画,讨论了它的同调性质.证得:若P是wk-正则半模,则P是弱单投射半模当且仅当P是投射半模.进一步引入弱拟单投射半模的概念,在R是加法可消且是完全可减的情况下,给出弱拟单投射半模的等价条件.The concept of weak simple projective semimodules was introduced.Some equivalent conditions and some characteristics of weak simple projective semimodules were given,homological properties were obtained.It was showed that if P was a wk-regular semimodule,then P was weak simple projective semimodules if and only if P was projective.The notion of weak quasi simple projective semi-modules was defined.And two equivalent conditions to weak quasi simple projective semimodules on a cancellative completely subtractive semiring R were given.

关 键 词：弱单投射半模 饱和同态 wk-正则半模 弱拟单投射半模. 

分 类 号：O153.3[理学—数学]