Krull dimension of tensor products of pullbacks

This 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$(A\otimes_kB)$ 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.