Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 2, pp. 449-479 (2008)

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Multiplication modules and homogeneous idealization III

Majid M. Ali

Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, P.C. 123, Al-Khod, Sultanate of Oman, e-mail:

Abstract: In our recent work we gave a treatment of certain aspects of multiplication modules, projective modules, flat modules and cancellation-like modules via idealization. The purpose of this work is to continue our study and develop the tool of idealization, particularly in the context of closed, divisible injective, and simple modules. We determine when a ring $R\left( M\right) $, the idealization of $M$, is a quasi-Frobenius or a distinguished ring. We also introduce and investigate the concept of $M$-$\frac{1}{2}$ (weak) cancellation ideals.

Keywords: closed submodule, divisible module, multiplication module, quasi-Frobenius ring

Classification (MSC2000): 13C13, 13C05, 13A15

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Electronic version published on: 18 Sep 2008. This page was last modified: 28 Jan 2013.

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