On automorphism-invariant modules

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

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.14, sa.5, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 5
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1142/s0219498815500747
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Automorphism-invariant module, pseudo-injective module, quasi-injective module, CS modules, RINGS
  • Gazi Üniversitesi Adresli: Hayır

Özet

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.