Differential polynomial rings which are generalized Asano prime rings

Abstract

Let R[x; 6] be a differential polynomialring over a prime Goldie ring R in an indeterminate x, where 6 is a derivation of R. In this paper, we describe explicitly the group of 6-stable v-R-ideals and using this results, we show that R[x; 6] is a generalized Asano primering if and only if R is a 6-generalized Asanoprimering.