t-e-A-injective module について

概要

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Using a essentially-A-injectivity, Oshiro extended relative injective modules. In this paper, we define the concept of a t-e-A-injective. module which is, in a some sense, essentially-A-injective module. from a torsion theoretic point of view. The following is our main theorem. Theorem The following statements are equivalent for a family of modules {M_α|α∈Λ}. (1) [○!+]__< α∈Λ>M_α is t-e-A-injective. (2) [○!+]__< α∈I>M_α is t-e-A-injective for any countable subset I ofΛ. (3)M_α is t-e-A-injective for any α∈Λ, and for every {M_<αi>, M_<α2>…}⊆{M_α|α∈Λ}andα∈Λ, with next condition (*), we choose any m_i∈M_<αi>(i=1,2,3…), then the ascending sequence [numerical formula] becomes stationary. (*)[numerical formula] (canonical homomorphism) and [numerical formula].
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