Resumen de Baer and quasi-Baer properties of group rings

Zhong Yi, Yiqiang Zhou

• 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-1R . 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-1R . 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.