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Baer and quasi-Baer properties of group rings

Part of: Homological methods Rings and algebras arising under various constructions

Published online by Cambridge University Press:  09 April 2009

Zhong Yi  and
Yiqiang Zhou
Zhong Yi
Affiliation:
Department of Mathematics, Guangxi Normal University, Guilin, 541004, P.R. Chinazyi@mailbox.gxnu.edu.cn
Yiqiang Zhou
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's A1C 5S7, Canadazhou@math.mun.ca
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Abstract

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A ring R is said to be a Baer (respectively, quasi-Baer) ring if the left annihilator of any nonempty subset (respectively, any ideal) of R is generated by an idempotent. It is first proved that for a ring R and a group G, if a group ring RG is (quasi-) Baer then so is R; if in addition G is finite then |G|–1 € R. Counter examples are then given to answer Hirano's question which asks whether the group ring RG is (quasi-) Baer if R is (quasi-) Baer and G is a finite group with |G|–1 € R. Further, efforts have been made towards answering the question of when the group ring RG of a finite group G is (quasi-) Baer, and various (quasi-) Baer group rings are identified. For the case where G is a group acting on R as automorphisms, some sufficient conditions are given for the fixed ring RG to be Baer.

MSC classification

Secondary: 16S34: Group rings , Laurent polynomial rings 16E50: von Neumann regular rings and generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 2 , October 2007 , pp. 285 - 296
Copyright
Copyright © Australian Mathematical Society 2007

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