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arXiv · 2402.05242

On some properties for cofiniteness of submonoids and ideals of an affine semigroup

Carmelo Cisto
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Abstract

Let $S$ and $\mathcal{C}$ be affine semigroups in $\mathbb{N}^d$ such that $S\subseteq \mathcal{C}$. We provide a characterization for the set $\mathcal{C}\setminus S$ to be finite, together with a procedure and computational tools to check whether such a set is finite and, if so, compute its elements. As a consequence of this result, we provide a characterization for an ideal $I$ of an affine semigroup $S$ so that $S\setminus I$ is a finite set. If so, we provide some procedures to compute the set $S\setminus I$.

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Carmelo Cisto. 2024-02-07. On some properties for cofiniteness of submonoids and ideals of an affine semigroup. https://arxiv.org/abs/2402.05242

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