MOD-RETRACTABLE RINGS


Kosan M. T. , Zemlicka J.

COMMUNICATIONS IN ALGEBRA, vol.42, no.3, pp.998-1010, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1080/00927872.2012.721430
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.998-1010
  • Keywords: Group module, Max rings, Noetherian rings, Nonsingular rings, Perfect rings, Retractable module, Semiartinian rings, 16D50, ENDOMORPHISM-RINGS, COMMUTATIVE RINGS, BAER MODULES, DIRECT SUMS, SUBMODULES

Abstract

A right module M over a ring R is said to be retractable if Hom(R)(M, N)0 for each nonzero submodule N of M. We show that M circle times(R)RG is a retractable RG-module if and only if M-R is retractable for every finite group G. The ring R is (finitely) mod-retractable if every (finitely generated) right R-module is retractable. Some comparisons between max rings, semiartinian rings, perfect rings, noetherian rings, nonsingular rings, and mod-retractable rings are investigated. In particular, we prove ring-theoretical criteria of right mod-retractability for classes of all commutative, left perfect, and right noetherian rings.