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.

Key Words:

• AF-domain
• Krull dimension
• Locally Jaffard ring
• Prime ideal
• Tensor product
• Valuative dimension

Mathematics Subject Classification:

• 13C15
• 13B24
• 13F05

Notes

Communicated by A. Facchini.