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Crossed products over prime rings

Crossed products over prime rings Abstract In this paper we obtain necessary and sufficient conditions for the crossed productR *G to be prime or semiprime under the assumption thatR is prime. The main techniques used are the Δ-methods which reduce these questions to the finite normal subgroups ofG and a study of theX-inner automorphisms ofR which enables us to handle these finite groups. In particular we show thatR *G is semiprime ifR has characteristic 0. Furthermore, ifR has characteristicp>0, thenR *G is semiprime if and only ifR *P is semiprime for all elementary abelianp-subgroupsP of Δ+(G) ∩G inn. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Israel Journal of Mathematics Springer Journals

Crossed products over prime rings

Israel Journal of Mathematics , Volume 31 (3): 33 – Sep 1, 1978

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References (9)

Publisher
Springer Journals
Copyright
1978 The Weizmann Science Press of Israel
ISSN
0021-2172
eISSN
1565-8511
DOI
10.1007/BF02761494
Publisher site
See Article on Publisher Site

Abstract

Abstract In this paper we obtain necessary and sufficient conditions for the crossed productR *G to be prime or semiprime under the assumption thatR is prime. The main techniques used are the Δ-methods which reduce these questions to the finite normal subgroups ofG and a study of theX-inner automorphisms ofR which enables us to handle these finite groups. In particular we show thatR *G is semiprime ifR has characteristic 0. Furthermore, ifR has characteristicp>0, thenR *G is semiprime if and only ifR *P is semiprime for all elementary abelianp-subgroupsP of Δ+(G) ∩G inn.

Journal

Israel Journal of MathematicsSpringer Journals

Published: Sep 1, 1978

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