2016/08/12 by Asensio, Pedro A. Guil, Tütünc\", Derya Keskin, Kalebogaz, Berke +1
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1608.03688
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.