Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583740 | Journal of Algebra | 2016 | 6 Pages |
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→Mf: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/Nφ:M→M/N can be lifted to an endomorphism of M.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pedro A. Guil Asensio, Derya Keskin Tütüncü, Berke Kalebog̃az, Ashish K. Srivastava,