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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
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Volume 19, Issue 2

Issues

Modules that have a supplement in every cofinite extension

Hamza Çalışıcı / Ergül Türkmen
Published Online: 2012-05-30 | DOI: https://doi.org/10.1515/gmj-2012-0018

Abstract.

Let R be a ring and M a left R-module. An R-module N is called a cofinite extension of M in case and is finitely generated. We say that M has the property CE (resp. CEE) if M has a supplement (resp. ample supplements) in every cofinite extension. In this study we give various properties of modules with these properties. We show that a module M has the property CEE iff every submodule of M has the property CE. A ring R is semiperfect iff every left R-module has the property CE. We also study cofinitely injective modules, direct summands of every cofinite extension, as a generalization of injective modules.

Keywords: Supplement; cofinite extension; semiperfect ring

About the article

Received: 2011-05-24

Revised: 2011-12-30

Published Online: 2012-05-30

Published in Print: 2012-06-01


Citation Information: Georgian Mathematical Journal, Volume 19, Issue 2, Pages 209–216, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2012-0018.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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