SKEW POLYNOMIAL RINGS WHICH ARE GENERALIZED ASANO PRIME RINGS

Abstract

Let R be a prime Goldie ring with quotient ring Q and σ be an automorphism of R. We define (σ-) generalized Asano prime rings and prove that a skew polynomial ring R[x; σ] is a generalized Asano prime ring if and only if R is a σ-generalized Asano prime ring. This is done by giving explicitly the structure of all v-ideals of R[x; σ] in case R is a σ-Krull prime ring. We provide some examples of σ-generalized Asano prime rings which are not Krull prime rings.