相关于挠理论的C12模

C12 Modules Relative to a Hereditary Torsion Theory

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.