Abstract
A ring R is called right principally quasi-Baer (simply, right p.q.-Baer) if the right annihilator of every principal right ideal of R is generated by an idempotent. For a ring R, let G be a finite group of ring automorphisms of R. We denote the fixed ring of R under G by RG. In this work, we investigated the right p.q.-Baer property of fixed rings under finite group action. Assume that R is a semiprime ring with a finite group G of X-outer ring automorphisms of R. Then we show that: 1) If R is G-p.q.-Baer, then RG is p.q.-Baer; 2) If R is p.q.-Baer, then RG are p.q.-Baer.
Highlights
Throughout this paper all rings are associative with identity
A ring R is called right principally quasi-Baer if the right annihilator of every principal right ideal of R is generated by an idempotent
We investigated the right p.q.-Baer property of fixed rings under finite group action
Summary
Recall from [1] that a ring R is called right principally quasi-Baer (right p.q.-Baer) if the right annihilator of every principal right ideal of R is generated, as a right ideal, by an idempotent of R. Recall from [7] (see [8]) that a ring R is called quasi-Baer if the right annihilator of every right ideal is generated, as a right ideal, by an idempotent of R. According to [9] an idempotent e of a ring R is called left (resp., right) semicentral if ae eae (resp., ea eae ) for all a R. For a ring R, we let Sl R (resp., Sl R ) denote the set of all left (resp., right) semicentral idempotents.
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