Seidenberg's Inequalities for Tensor Products of Algebras

ABSTRACT

This paper is concerned with the study of the Krull dimension of tensor products of algebras over a field k. More precisely, we seek satisfactory analogues of Seidenberg's inequalities of polynomial rings for tensor products of k-algebras. As an application, we supply a new range of k-algebras A and B for which the Krull dimension of A ⊗  _k B may be computed.

Key Words:

• AF-domain
• Krull dimension
• Polynomial ring
• Pullbacks
• Tensor product
• Transcendence degree

Mathematics Subject Classification:

• 13C15
• 13B24
• 13F05

Notes

^#Communicated by A. Facchini.