Row-Factorization Matrices in Arf Numerical Semigroups and Defining Ideals
Meral S\"uer, Mehmet Ye\c{s}il
TL;DR
This paper explores row-factorization matrices in Arf numerical semigroups, providing a comprehensive list for specific cases, and uses this to identify generators of their defining ideals and analyze their generic properties.
Contribution
It offers a complete classification of row-factorization matrices for certain Arf numerical semigroups and applies this to determine their defining ideal generators.
Findings
List of row-factorization matrices for specific Arf semigroups
Identification of generators of defining ideals
Analysis of generic properties of these matrices
Abstract
In this paper, we investigate the row-factorization matrices of Arf numerical semigroups, and we provide the full list of such matrices of certain Arf numerical semigroups. We use the information of row-factorization matrices to detect the generic nature and to find generators of the defining ideals.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Advanced Algebra and Logic