On the completed tensor product of two preadic algebras over a field

TL;DR

This paper investigates how properties of preadic noetherian algebras over a field are preserved or transferred through their completed tensor product, addressing a problem initiated by Grothendieck.

Contribution

It provides new insights into the transfer of algebraic properties in completed tensor products of preadic noetherian algebras over a field.

Findings

Established conditions for property transfer in completed tensor products

Extended Grothendieck's problem to broader classes of algebras

Identified key factors influencing property preservation

Abstract

In this paper, we study the problem, initiated by Grothendieck, of the transfer of the properties of two preadic noetherian algebras over a field to their completed tensor product.