相关于挠理论的C12模  

C12 Modules Relative to a Hereditary Torsion Theory

作　　者：李煜彦[1] LI Yu-yan(School of Mathematics and Information,Longnan Teachers College,Chengxian Gansu 742500)

机构地区：[1]陇南师范高等专科学校数信学院,甘肃成县742500

出　　处：《甘肃高师学报》2020年第5期1-3,共3页Journal of Gansu Normal Colleges

基　　金：甘肃省高等学校创新基金项目“有限n-表示模及相关问题的研究”(2020A-277).

摘　　要：设τ是遗传挠理论,提出了τ-C12模的概念,它是C12模的推广.称M是τ-C12模.如果对M的任意τ-稠密子模N,存在M的直和因子K以及单同态f:N→K,使得f(N)≤τ-eK.给出了τ-C12模的一个等价刻画,讨论了τ-C11模和τ-C12模之间的关系,证明了任意一个模都同构于某个τ-C12模的直和因子.Letτbe a hereditary torsion theory.In this paper,the concept ofτ-C12 module is introduced,which is a generalization of C12 module.A module M is calledτ-C12 module,if for every submodule N of M,there exists a direct summand K of M and a monomorphism f:N→K,such that f(N)is anτ-essential submodule of K.A equivalent characterization ofτ-C12 module is given,the relationship ofτ-C11 module andτ-C12 module is discussed,and it is proved that any module is isomorphic to a direct summand of a module which satisfiesτ-C12.

关 键 词：遗传挠理论 τ-C12模 τ-补 直和因子 

分 类 号：O153.3[理学—数学]