Optimal parametrizations and valuations

Document Type

Journal Article

Role

Author

Published In

Communications in Algebra

Publication Date

7-16-2026

Abstract

This article discusses a way for uniquely setting up the valuations for the minimal generators of the maximal ideal of a one dimensional complete reduced and irreducible local algebra over an algebraically closed field, when treated as a subring of its integral closure. Our observations are a generalization of the more well-studied case of a numerical semigroup ring. These results provide completion to some missing arguments in certain proofs present in the existing literature, including some results concerning a long-standing conjecture of R. Berger.

Comments

Preprint version available on arXiv.

Keywords

Berger conjecture, Herzog-Kunz generators, valuation semigroup

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