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arXiv · 1608.03688

Modules which are coinvariant under automorphisms of their projective covers

Pedro A. Guil Asensio·Derya Keskin Tütünc\"·Berke Kalebogaz·Ashish K. Srivastava
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Abstract

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 $f:N\rightarrow M$ 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 $\varphi: M\rightarrow M/N$ can be lifted to an endomorphism of $M$.

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Pedro A. Guil Asensio, Derya Keskin Tütünc\", Berke Kalebogaz, Ashish K. Srivastava. 2016-08-12. Modules which are coinvariant under automorphisms of their projective covers. https://arxiv.org/abs/1608.03688

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