The Milnor Number of One Dimensional Local Rings

Abstract

In this paper we present an analogue of the Milnor number for one dimensional local ring, and we show that it satisfies analogous properties to those of the Milnor number of plane curves over a field. In addition, we present two analogues of the semi-group of values for a one dimensional ring and show how they relate to our Milnor number. Finally, we use these tools and techniques to show we can relate these semigroups of one dimensional rings of finite Cohen-Macaulay type to those of the classical ADE singularities.