Abstract
In this paper, the (quasi-)Baerness of skew group ring and fixed ring is investigated. The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, then R G is a Baer ring; if R is an Artinian simple ring with identity and G an outer automorphism group, then RG is a Baer ring. Moreover, by decomposing Morita Context ring and Morita Context Theory, we provided several conditions of Morita Context ring, which is formed of skew group ring and fixed ring, to be (quasi-)Baer ring.
Highlights
Throughout this paper all rings are associative with identity, all modules are unitary module
The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, R G is a Baer ring; if R is an Artinian simple ring with identity and G an outer automorphism group, RG is a Baer ring
By decomposing Morita Context ring and Morita Context Theory, we provided several conditions of Morita Context ring, which is formed of skew group ring and fixed ring, to beBaer ring
Summary
Throughout this paper all rings are associative with identity, all modules are unitary module. Recall that a ring R is called (quasi-)Baer if the right annihilator of every nonempty subset Left) principally quasi-Baer ring (right p.q.-Baer ring) if the right A ring R is called p.q.-Baer if R is both right and left p.q.-Baer [1]. By [1], we know that if R is a semiprime p.q.-Baer ring with a finite group G of X-outer ring automorphisms of R , R G is a p.q.-Baer ring. In [1] example of a semiprime Baer ring R with G a finite group of X-outer ring automorphisms of R such that R has no nonzero G -torsion, but R G is not a Baer ring was provided
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