Associated prime ideals over skew PBW extensions

Abstract

In this article, we continue the study of ideals of the noncommutative rings of polynomial type known as skew Poincaré-Birkhoff-Witt extensions. More exactly, we focus on the associated prime ideals of these extensions. Our purpose here is to describe how the associated primes of a ring of coefficients behave under passage to a skew PBW extension over this ring. As we show, all results established here coincide and generalize those corresponding in the commutative case and the Ore extensions.