On Modules Over Group Rings
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- 作者：M. Tamer Ko艧an (1)
Tsiu-Kwen Lee (2)
Yiqiang Zhou (3) - 关键词：Group ring ; Group module ; Maschke鈥檚 Theorem ; Semisimple module ; Regular module ; Injective module ; FP ; injective module ; Primary 16S34 ; Secondary 16D50 ; 16D60 ; 16E50
- 刊名：Algebras and Representation Theory
- 出版年：2014
- 出版时间：February 2014
- 年：2014
- 卷：17
- 期：1
- 页码：87-102
- 全文大小：398 KB
- 作者单位：M. Tamer Ko艧an (1)
Tsiu-Kwen Lee (2)
Yiqiang Zhou (3)
1. Department of Mathematics, Gebze Institute of Technology, Gebze/Kocaeli, Turkey
2. Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan
3. Department of Mathematics and Statistics, Memorial University of Newfoundland, St.John鈥檚, Nfld A1C 5S7, Canada - ISSN：1572-9079
文摘
Let M be a right module over a ring R and let G be a group. The set MG of all formal finite sums of the form 鈭戔€?sub class="a-plus-plus"> g鈥夆垐鈥?em class="a-plus-plus">G m g g where m g 鈥夆垐鈥?em class="a-plus-plus">M becomes a right module over the group ring RG under addition and scalar multiplication similar to the addition and multiplication of a group ring. In this paper, we study basic properties of the RG-module MG, and characterize module properties of (MG) RG in terms of properties of M R and G. Particularly, we prove the module-theoretic versions of several well-known results on group rings, including Maschke鈥檚 Theorem and the classical characterizations of right self-injective group rings and of von Neumann regular group rings.