Abstract
A ring R is called left p.q.-Baer if the left annihilator of a principal left ideal is generated, as a left ideal, by an idempotent. It is first proved that for a ring R and a group G, if the group ring RG is left p.q.-Baer then so is R; if in condition G is finite then |G|−1 ∈ R. Counterexamples are given to answer the question whether the group ring RG is left p.q.-Baer if R is left p.q.-Baer and G is a finite group with |G|−1 ∈ R. Further, RD∞ is left p.q.-Baer if and only if R is left p.q.-Baer.
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