On automorphism-invariant modules


Truong Cong Quynh T. C. Q. , Kosan M. T.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.14, no.5, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 5
  • Publication Date: 2015
  • Doi Number: 10.1142/s0219498815500747
  • Title of Journal : JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Abstract

Let M and N be two modules. M is called automorphism N-invariant if for any essential submodule A of N, any essential monomorphism f : A -> M can be extended to some g is an element of Hom(N, M). M is called automorphism-invariant if M is automorphism M-invariant. This notion is motivated by automorphism-invariant modules analog discussed in a recent paper by Lee and Zhou [Modules which are invariant under automorphisms of their injective hulls, J. Algebra Appl. 12(2) (2013), 1250159, 9 pp.]. Basic properties of mutually automorphism-invariant modules and automorphism-invariant modules are proved and their connections with pseudo-injective modules are addressed.