Article ID Journal Published Year Pages File Type
4587519 Journal of Algebra 2008 13 Pages PDF
Abstract

We constructively prove that for any ring R with Krull dimension ⩽d, the ring R〈X〉 locally behaves like the ring R(X) or a localization of a polynomial ring of type (S−1R)[X] with S a multiplicative subset of R such that the Krull dimension of S−1R is ⩽d−1. As an application, we give a simple and constructive proof of the Lequain–Simis Induction Theorem which is an important variation of the Quillen Induction Theorem.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory