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# Group Actions on Quasi-Baer Rings

Published:2009-12-01
Printed: Dec 2009
• Hai Lan Jin
• Jaekyung Doh
• Jae Keol Park
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## Abstract

A ring $R$ is called {\it quasi-Baer} if the right annihilator of every right ideal of $R$ is generated by an idempotent as a right ideal. We investigate the quasi-Baer property of skew group rings and fixed rings under a finite group action on a semiprime ring and their applications to $C^*$-algebras. Various examples to illustrate and delimit our results are provided.
 Keywords: (quasi-) Baer ring, fixed ring, skew group ring, $C^*$-algebra, local multiplier algebra
 MSC Classifications: 16S35 - Twisted and skew group rings, crossed products 16W22 - Actions of groups and semigroups; invariant theory 16S90 - Torsion theories; radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx} 16W20 - Automorphisms and endomorphisms 16U70 - Center, normalizer (invariant elements)