Partial Skew Polynomial Rings Over Semisimple Artinian Rings

Abstract

Let R be a semisimple Artinian ring with a partial action α of ℤ on R, and let R[x; α] be the partial skew polynomial ring. By the classification of the set E of all minimal central idempotents in R into three different types, a complete description of the prime radical of R[x; α] is given. Moreover, it is shown that any nonzero prime ideal of R[x; α] is maximal and is either principal or idempotent. In the case where α is of finite type, it is shown that R[x; α] is a semiprime hereditary ring.