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International Journal of Mathematics and Mathematical Sciences
Volume 2015, Article ID 879129, 6 pages
Research Article

PS-Modules over Ore Extensions and Skew Generalized Power Series Rings

1Mathematics Department, Faculty of Science, Al-Azhar University, P.O. Box 11884, Nasr City, Cairo, Egypt
2Department of Mathematics and Statistics, Faculty of Science, Taif University, P.O. Box 888, Al-Hawiyah, Taif 21974, Saudi Arabia
3Department of Mathematics, Faculty of Science, Ain Shams University, P.O. Box 11566, Abbasaya, Cairo, Egypt

Received 7 December 2014; Revised 9 March 2015; Accepted 11 March 2015

Academic Editor: Ram N. Mohapatra

Copyright © 2015 Refaat M. Salem et al. 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.


A right -module is called a PS-module if its socle, , is projective. We investigate PS-modules over Ore extension and skew generalized power series extension. Let be an associative ring with identity, a unitary right -module, Ore extension, a right -module, a strictly ordered additive monoid, a monoid homomorphism, the skew generalized power series ring, and the skew generalized power series module. Then, under some certain conditions, we prove the following: (1) If is a right PS-module, then is a right PS-module. (2) If is a right PS-module, then is a right PS-module.