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Group Actions on Quasi-Baer Rings |
Published:2009-12-01
Printed: Dec 2009
Printed: Dec 2009
- Hai Lan Jin
- Jaekyung Doh
- Jae Keol Park
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) |