Automorphism-Invariant Modules

Asensio, Pedro A. Guil; Srivastava, Ashish Kumar

doi:10.1090/conm/634/12688

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Cited by 10 publications

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“…Automorphism-invariant modules have been studied extensively in [1,4,5,8,9,10,14,16]. On the other hand, it was proved in [5] that a module M is automorphisminvariant if and only if any monomorphism from a submodule N of M to M extends to an endomorphism of M .…”

Section: Introductionmentioning

confidence: 99%

Modules which are coinvariant under automorphisms of their projective covers

et al. 2016

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In this paper we study modules coinvariant under automorphisms of their projective covers. We first provide an alternative, and in fact, a more succinct and conceptual proof for the result that a module M is invariant under automorphisms of its injective envelope if and only if given any submodule N of M , any monomorphism f : N → M can be extended to an endomorphism of M and then, as a dual of it, we show that over a right perfect ring, a module M is coinvariant under automorphisms of its projective cover if and only if for every submodule N of M , any epimorphism ϕ : M → M/N can be lifted to an endomorphism of M .2010 Mathematics Subject Classification. 16D40, 16D80.

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