Modules with ADS-(pre)envelopes and ADS-(pro)covers


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

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.17, no.5, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.1142/s0219498818500962
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: ADS module, (pre)envelope, (pre)cover, Noetherian ring, V-ring, ADS MODULES, RINGS
  • Gazi University Affiliated: No

Abstract

This paper focusses on the question of when modules have ADS- preenvelopes and covers. For a ring R, it is proved that every ADS module over R is injective if and only if every right R-module has an ADS-(pre)envelope (an ADS-(pre)cover). In this paper, we also introduce a generalization of ADS modules stated in terms of their invariance under certain automorphisms of their envelopes.