The Milnor Number of One Dimensional Local Rings
Abstract
We present an analogue of the Milnor number for one dimensional local ring inspired by Milnor's formula, and we show that it satisfies analogous properties to those of the classical Milnor number of curves over a field. In addition, we study two analogues of the semigroup of values of a one dimensional ring and show how they relate to our Milnor number. Finally, we use these tools to classify one dimensional rings of finite Cohen-Macaulay type based upon their semigroups and relate these semigroups to those of the classical ADE singularities.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Algebraic Geometry and Number Theory
Rings
Modules
and Algebras
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 February 2026
- Language
- EN
- Document type
- Preprint