TITLE:
The p.q.-Baer Property of Fixed Rings under Finite Group Action
AUTHORS:
Ling Jin, Hailan Jin
KEYWORDS:
p.q.-Baer Property; Fixed Ring; Group Action
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.6,
November
12,
2012
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.