广义逆多项式模的co-Hopf性质

Co-Hopfian Modules of Generalized Inverse Polynomials

设R是结合环(可以没有单位元),(S,≤)是严格全序幺半群,序≤是Artin的且对任意s∈S,有0≤s,则对任意具有性质(F)的左R-模M,[MS,≤]是co-Hopf左[[RS,≤]]一模当且仅当M是co-Hopf左R-模.

Let R be an associative ring not necessarily possessing an identity, and (S, ≤) a strictly totally ordered monoid which is also artinian and satisfies that 0 ≤ s for any s ∈ S. Assume that M is a left .R-module having property (F). It is shown that M is a co-Hopfian left R-module if and only if [MS,≤] is a co-Hopfian left [[RS,≤]]-module.