Table of Contents
Algebra
Volume 2015, Article ID 595274, 4 pages
http://dx.doi.org/10.1155/2015/595274
Research Article

Generalized Malcev-Neumann Series Modules with the Beachy-Blair Condition

1Department of Mathematics and Statistics, Faculty of Science, Taif University, P.O. Box 888, Al-Hawiyah, Taif 21974, Saudi Arabia
2Mathematics Department, Faculty of Science, Al-Azhar University, P.O. Box 11884, Nasr City, Cairo, Egypt

Received 9 January 2015; Revised 9 March 2015; Accepted 10 March 2015

Academic Editor: Andrei V. Kelarev

Copyright © 2015 Mohamed A. Farahat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a new class of extension rings called the generalized Malcev-Neumann series ring with coefficients in a ring and exponents in a strictly ordered monoid which extends the usual construction of Malcev-Neumann series rings. Ouyang et al. in 2014 introduced the modules with the Beachy-Blair condition as follows: A right -module satisfies the right Beachy-Blair condition if each of its faithful submodules is cofaithful. In this paper, we study the relationship between the right Beachy-Blair condition of a right -module and its Malcev-Neumann series module extension .