The p.q.-Baer Property of Fixed Rings under Finite Group Action

Ling Jin, Hailan Jin

Department of Mathematics, College of Sciences, Yanbian University, Yanji, China.

DOI: 10.4236/apm.2012.26059                

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 R^G. 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 R^G is p.q.-Baer; 2) If R is p.q.-Baer, then R^G are p.q.-Baer.

Keywords

p.q.-Baer Property; Fixed Ring; Group Action

Conflicts of Interest

The authors declare no conflicts of interest.

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