A CHARACTERIZATION OF GOLDIE EXTENDING MODULES OVER DEDEKIND DOMAINS


AKALAN E., Birkenmeier G. F. , TERCAN A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.10, no.6, pp.1291-1299, 2011 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 6
  • Publication Date: 2011
  • Doi Number: 10.1142/s0219498811005178
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1291-1299

Abstract

In this paper, we characterize G-extending (Goldie extending) modules over Dedekind domains and we use the G-extending condition to characterize the modules over a principal ideal domain whose pure submodules are direct summands. Moreover, we show that if R is a principal ideal domain, then the class of G-extending modules is closed under direct summands and that if R is a Dedekind domain, then the class of G-extending torsion modules is closed under finite direct sums.