J. Aust. Math. Soc. 83 (2007), no. 2, pp. 285–296.

Baer and quasi-Baer properties of group rings

Zhong Yi Yiqiang Zhou
Department of Mathematics
Guangxi Normal University
Guilin, 541004
P.R. China
Department of Mathematics and Statistics
Memorial University of Newfoundland
St. John's A1C 5S7
Received 1 November 2005; revised 1 May 2006
Communicated by J. Du


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}\in 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}\in 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 R^G to be Baer.

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2000 Mathematics Subject Classification: primary 16S34; secondary 16E50
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