IJPAM: Volume 95, No. 3 (2014)


Burcu Nişancı Türkmen
Department of Mathematics
Faculty of Art and Science
Amasya University
Ipekkoy Amasya, TURKEY

Abstract. In this paper, we study on cofinitely $Rad$-lifting modules as a proper generalization of modules with the property $(P^{*})$ and cofinitely lifting modules, and we obtain the properties of these modules. In particular, we prove that if $M$ with the property $(SSP)$ is a cofinitely $Rad$-lifting module, then $\frac{M}{N}$ is a cofinitely $Rad$-lifting module for every direct summand $N$ of $M$. We show that $\pi$-projective cofinitely ($Rad$-) $\oplus$-supplemented modules are cofinitely ($Rad$-) lifting. We obtain a new characterization of semiperfect rings by using this result. This characterization generalizes the result of Wang and Wu.

Received: May 24, 2014

AMS Subject Classification: 16D10, 16N80

Key Words and Phrases: cofinite submodule, lifting module, the property $(P^{*})$, cofinitely $Rad$-lifting, semiperfect ring

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DOI: 10.12732/ijpam.v95i3.11 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 95
Issue: 3
Pages: 453 - 461

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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).