2025/01/27 by Fuensanta Aroca, Annel Ayala, Aroca, Fuensanta +5
Decision Sciences · Mathematics · #Advanced Topics in Algebra #Functional Equations Stability Results #Fuzzy and Soft Set Theory #Mathematics #Pure mathematics
paper · pdf · doi:10.48550/arxiv.2501.16552
openalex publication_date 2025/01/27 · openalex created_date 2025/01/30 · openalex updated_date 2026/07/28
For an arbitrary hypersurface singularity, we construct a family of semigroups associated with algebraically closed fields that arise as an infinite union of rings of series. These semigroups extend the value semigroup of a plane curve studied by Abhyankar and Moh. The algebraically closed fields under consideration possess a natural valuation that induces a corresponding value semigroup. We establish the necessary conditions under which these semigroups are independent of the choice of the root. Moreover, the extensions proposed by P. González and Kiyek-Micus, where González specifically addresses the case of quasi-ordinary singularities, and the extension introduced by Abbas-Assi, can be understood as particular instances within our constructed family.