Nilpotent-invariant modules and rings

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

COMMUNICATIONS IN ALGEBRA, cilt.45, sa.7, ss.2775-2782, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 7
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/00927872.2016.1226873
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2775-2782
  • Anahtar Kelimeler: Automorphism-invariant, module, nilpotent endomorphism, nilpotent-invariant module
  • Gazi Üniversitesi Adresli: Hayır

Özet

Automorphism-invariant modules, due to Lee and Zhou, generalize the notion of quasi-injective modules. A module which is invariant under automorphisms of its injective hull is called an automorphism-invariant module. Here we carry out a study of the module which is invariant under nilpotent endomorphisms of its injective envelope, such as modules are called nilpotent-invariant. Many basic properties are obtained. For instance, it is proved that (1) nilpotent-invariant modules have the (C3) property, (2) if M = M-1 circle plus M-2 is nilpotent-invariant, then M-1 and M-2 are relative injective. In this paper, we also show that (3) a simple right nilpotent-invariant ring R is either right self-injective or R-R is uniform square-free.