2012/08/24 by S. Singh, Surjeet Singh, Singh, S. +2 · 1 citation
Mathematics · #16D50 #16P40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16D50 #msc:16P40
paper · pdf · doi:10.48550/arxiv.1208.4996
To appear in Journal of Algebra
arxiv created 2012/08/24 · openalex publication_date 2012/08/24 · arxiv updated 2012/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A module M is called an automorphism-invariant module if every isomorphism between two essential submodules of M extends to an automorphism of M. This paper introduces the notion of dual of such modules. We call a module M to be a dual automorphism-invariant module if whenever K1 and K2 are small submodules of M, then any epimorphism η:M/K1→ M/K2 with small kernel lifts to an endomorphism φ of M. In this paper we give various examples of dual automorphism-invariant module and study its properties. In particular, we study abelian groups and prove that dual automorphism-invariant abelian groups must be reduced. It is shown that over a right perfect ring R, a lifting right R-module M is dual automorphism-invariant if and only if M is quasi-projective.