Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 2, pp. 449479 (2008) 

Multiplication modules and homogeneous idealization IIIMajid M. AliDepartment of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, P.C. 123, AlKhod, Sultanate of Oman, email: mali@squ.edu.omAbstract: In our recent work we gave a treatment of certain aspects of multiplication modules, projective modules, flat modules and cancellationlike 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 quasiFrobenius 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, quasiFrobenius ring Classification (MSC2000): 13C13, 13C05, 13A15 Full text of the article:
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