Semiprime skew group rings

Infinite crossed products and group-graded rings

“…S. Montgomery [9] proved that if R is prime (or semiprime) and G is X-outer on R, then R * G is prime (or semiprime, respectively). In [6], J. Fisher and S. Montgomery settled the semiprime question for G finite. Infinite groups were considered by S. Montgomery and the author in [10] where the A-methods and the techniques of [6] combined to handle the case where R is a prime ring.…”

“…In [6], J. Fisher and S. Montgomery settled the semiprime question for G finite. Infinite groups were considered by S. Montgomery and the author in [10] where the A-methods and the techniques of [6] combined to handle the case where R is a prime ring. This was extended in [16] to semiprime coefficient rings and then the problem was essentially solved in [18].…”

A Morita context related to finite automorphism groups of rings

“…They used this result to prove the important: THEOREM 0.2 [8]. Let R be a semiprime ring and G a finite group of automorphisms of R. If either R has no \G\-torsion or G is X-outer then S is semiprime.…”

“…Now, if R is primitive then so is S [8], hence so is R G . (d) and (e) follows from Theorems 1.23 and 1.19 respectively.…”

“…By Fisher and Montgomery [8], S is semiprime in both, and in case (1) R is Sfaithful. Moreover, if in case (1) R is G-prime, primitive or <yK(R) = 0, with Λ^C) as above, then the same is true for S. Hence if R enjoys one of these properties so does R G [Theorem 2.3].…”