Lifting Ideals in Noncommutative Integral Extensions

Abstract

This note is intended as a commentary on a part of the paper [1] by Gulliksen, Ribenboim, and Viswanathan. It takes its inspiration from a colloquium talk by P. Ribenboim.Our aim is a partial generalization of the theorem of Cohen-Seidenberg (cf. [2], IX. 1, Propositions 9 and 10) to noncommutative algebras.Definition. Let A be a ring with 1 in the center of another ring B (with the same 1). B is said to be integral over A, if each element b ∊ B satisfies an integral equation