Commutative Ring Theory

7 Radices in Commutative Rings

Douglas L. Costa and Gordon E. Keller¹ Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903-3199 USA.

0. Introduction

Recent research by the authors [4,6] has shown that a structure, which they have named a radix, in commutative rings plays a fundamental role in the classification of normal subgroups of the special linear group. The purpose of this article is to introduce the notion of a radix to commutative algebraists, to explain how radices arose naturally, to show that they behave in some ways that commutative algebraists might consider “natural,” and to suggest that it might prove fruitful for commutative ring theorists to examine structures more general than ideals.

1. What ...