On Krull and valuative dimension of tensor products of algebras

摘要

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 circle times(k) B when A and B are k-algebras such that the polynomial ring An is an AF-domain for some positive integer n . Also, we compute dim v (A circle times(k) B) in the case where A subset of B .