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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 (quasi-) Baer ring, fixed ring, skew group ring, $C^*$-algebra, local multiplier algebra
MSC Classifications: 16S35, 16W22, 16S90, 16W20, 16U70 show english descriptions Twisted and skew group rings, crossed products
Actions of groups and semigroups; invariant theory
Torsion theories; radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}
Automorphisms and endomorphisms
Center, normalizer (invariant elements)
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)
 

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