Factorizations in Numerical Semigroup Algebras

TL;DR

This paper investigates the algebraic structure of numerical semigroup rings, focusing on factorizations and conditions for complete intersection properties, especially in flat rectangular algebras generated by few monomials.

Contribution

It introduces new methods to analyze factorizations in numerical semigroup algebras and characterizes when such algebras are complete intersections.

Findings

Characterization of factorizations in numerical semigroup algebras

Conditions for flat rectangular algebras to be complete intersections

Explicit analysis of algebras generated by few monomials

Abstract

We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The complete intersection property of numerical semigroup algebras is investigated using factorizations of monomials into minimal ones. The goal is to study whether a flat rectangular algebra is a complete intersection. Along this direction, special types of algebras generated by few monomials are worked out in detail.