On Krull and Valuative Dimension of Tensor Products of Algebras

Abstract

This article is concerned with the dimension theory of tensor products of algebras over a field k. In fact, we provide formulas for the Krull and valuative dimension of A⊗ k B when A and B are k-algebras such that the polynomial ring A[n] is an AF-domain for some positive integer n. Also, we compute dim v (A⊗ k B) in the case where A ⊆ B.