CHARACTERIZATIONS OFRad-SUPPLEMENTED MODULES

Turkmen E., Pancar A.

MISKOLC MATHEMATICAL NOTES, vol.13, no.2, pp.569-580, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.18514/mmn.2012.397
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.569-580
  • Keywords: Rad-supplement, Rad-supplemented module, extension, semilocal ring, artinian principal ideal ring, SEMIPERFECT
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

We prove that a commutative ring R is an artinian principal ideal ring if and only if the ring is semilocal and every Rad-supplemented R-module is a direct sum of w-local R-modules. Moreover, we study of extensions of Rad-supplemented modules over commutative noetherian rings, and we show that if M/N is reduced, M is Rad-supplemented if and only if N and M/N are Rad-supplemented. We also prove that over a dedekind domain an indecomposable, amply Rad-supplemented radical module is hollow radical.