On the ideal of some sumset semigroups
J. I. Garc\'ia-Garc\'ia, D. Mar\'in-Arag\'on, A. Vigneron-Tenorio
TL;DR
This paper introduces an algorithm to compute ideals in sumset semigroups, enabling the analysis of their factorization and additive properties, thus bridging computational algebra and additive number theory.
Contribution
It provides a novel algorithm for computing ideals in sumset semigroups and explores their factorization and additive properties.
Findings
Algorithm successfully computes ideals in sumset semigroups
Reveals new insights into factorization properties
Links computational algebra with additive number theory
Abstract
A sumset semigroup is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. In this work, an algorithm for computing the ideals associated with some sumset semigroups is provided. Using these ideals, we study some factorization properties of sumset semigroups and some additive properties of sumsets. This approach links computational commutative algebra with additive number theory.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · semigroups and automata theory