Regularity of tensor products of k-algebras

TL;DR

This paper investigates when the regularity property of algebras over a field k is preserved under tensor products, providing necessary and sufficient conditions especially for Noetherian tensor products of extension fields.

Contribution

It establishes precise criteria for the transfer of regularity in tensor products of k-algebras, particularly for extension fields, advancing understanding in algebraic regularity transfer.

Findings

Necessary and sufficient conditions for regularity transfer in tensor products

Characterization of regularity in Noetherian tensor products of extension fields

Examples illustrating the scope and limitations of the results

Abstract

This paper tackles a problem on the possible transfer of regularity to tensor products of algebras over a field k. The main result establishes necessary and sufficient conditions for a Noetherian tensor product of two extension fields of k to inherit regularity in various settings of separability. Thereby, we provide some applications as well as several original examples to illustrate or delimit the scope of the established results.