Table of Contents
Algebra
Volume 2014, Article ID 256020, 5 pages
http://dx.doi.org/10.1155/2014/256020
Research Article

Finitely Generated Modules over Group Rings of a Direct Product of Two Cyclic Groups

Department of Mathematics and Informatics, Faculty of Science Dhar Mahraz, Sidi Mohamed Ben Abdellah University, 30000 Fez, Morocco

Received 27 August 2014; Accepted 15 November 2014; Published 1 December 2014

Academic Editor: Zhongshan Li

Copyright © 2014 Ahmed Najim and Mohammed Elhassani Charkani. 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

Let be a commutative field of characteristic and let , where and are two finite cyclic groups. We give some structure results of finitely generated -modules in the case where the order of is divisible by . Extensions of modules are also investigated. Based on these extensions and in the same previous case, we show that -modules satisfying some conditions have a fairly simple form.