Abstract
A ring R is said to be a Baer (respectively, quasiBaer) 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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