A generalization of Azumaya's theorem on $M$-injective modules
---Publisher, magazine: ,
Publication year: 2005
Lưu Trích dẫn Chia sẻAbstract
Let L be a finitely generated right R-module. We prove that if M is Lgenerated and {Nα|α ∈ Λ} a family of M-injective modules, then L α∈Λ Nα is Minjective if and only if for any choice of fαi : L → Nαi (αi ∈ Λ, i ∈ N) such that T i∈N Kerfαi ⊃ Kerf for some f : L → M, the ascending chain T i≥n Kerfαi (n ∈ N) becomes stationary. This result can be regarded as a generalized theorem of Azumaya on M-injective modules.
Tags: M-injective module; M-generated module; Essential and Singular submodule; Injective hull.
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A generalization of Azumaya's theorem on $M$-injective modules