Krull Dimension of Tensor Products of Pullbacks

Abstract

Communicated by A. FacchiniThis paper is concerned with the study of the dimension theory of tensor products of algebras over a field k. We answer an open problem set in [6] and compute dim(A ⊗ k B) when A is a k-algebra arising from a specific pullback construction involving AF-domains and B is an arbitrary k-algebra. On the other hand, we deal with the question (Q) set in [5] and show, in particular, that such a pullback A is in fact a generalized AF-domain.