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.
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Montgomery, S., Passman, D.S. Crossed products over prime rings. Israel J. Math. 31, 224–256 (1978). https://doi.org/10.1007/BF02761494
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DOI: https://doi.org/10.1007/BF02761494