  In this paper, we are concerned with the study of the dimension theory of
tensor products of algebras over a field $k$. We introduce and investigate the
notion of generalized AF-domain (GAF-domain for short) and prove that any
$k$-algebra $A$ such that the polynomial ring in one variable $A[X]$ is an
AF-domain is in fact a GAF-domain, in particular any AF-domain is a GAF-domain.
Moreover, we compute the Krull dimension of $A\otimes_kB$ for any $k$-algebra
$A$ such that $A[X]$ is an AF-domain and any $k$-algebra $B$ generalizing the
main theorem of Wadsworth in [16].
