We study the “q-commutative” power series ring R := kq[[x1, . . . , xn]], defined by the relations xixj = qijxjxi, for mulitiplicatively antisymmetric scalars qij in a field k. Our results provide a detailed account of prime ideal structure for a class of noncommutative, complete, local, noetherian domains having arbitrarily high (but finite) Krull, global, and classical Krull dimension. In par...

The main goal of this paper is to introduce and study new classes partial orderings on a set with Krull dimension at most 1. We show that these are related door, submaximal Whyburn T0-spaces.