ON (D-12)-MODULES

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Copy For Citation

Tutuncu D., TRIBAK R.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.43, no.4, pp.1355-1373, 2013 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 43 Issue: 4
• Publication Date: 2013
• Doi Number: 10.1216/rmj-2013-43-4-1355
• Journal Name: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.1355-1373
• Hacettepe University Affiliated: Yes

Abstract

is known that a direct summand of a (D-12)module need not be a (D-12)-module. In this paper we establish some properties of completely (D-12)-modules (modules for which every direct summand is a (D-12)-module). After giving some examples of completely (D-12)-modules, it is proved that every finitely generated weakly supplemented completely (D-12)-module is a finite direct sum of local modules. We also prove that a direct sum of (D-12)-modules need not be a (D-12)-module. Then we deal with some special cases of direct sums of (D-12)-modules. We conclude this work by characterizing some rings in terms of (D-12)-modules.