Finitely Generated Modules over Group Rings of a Direct Product of Two Cyclic Groups. (1st December 2014)

• Record Type: Journal Article
• Authors: Najim, Ahmed; Charkani, Mohammed Elhassani
• Other Names: Li Zhongshan Academic Editor.
• Is Part Of: Algebra. Volume 2014(2014)
• Publication Date: 2014-12-01
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2014/256020
• Languages: English
• ISSNs: 2314-4106

Abstract

Abstract : Let K be a commutative field of characteristic p > 0 and let G = G 1 × G 2, where G 1 and G 2 are two finite cyclic groups. We give some structure results of finitely generated K [ G ] -modules in the case where the order of G is divisible by p . Extensions of modules are also investigated. Based on these extensions and in the same previous case, we show that K [ G ] -modules satisfying some conditions have a fairly simple form.