A CHARACTERIZATION OF GOLDIE EXTENDING MODULES OVER DEDEKIND DOMAINS

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

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.10, no.6, pp.1291-1299, 2011 (SCI-Expanded)

• 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 (SCI-EXPANDED), Scopus
• Page Numbers: pp.1291-1299
• Hacettepe University Affiliated: Yes

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.