On some properties for cofiniteness of submonoids and ideals of an affine semigroup
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916118212378624 |
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| author | Cisto, Carmelo |
| author_facet | Cisto, Carmelo |
| contents | 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 $S\setminus I$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some properties for cofiniteness of submonoids and ideals of an affine semigroup Cisto, Carmelo Commutative Algebra 20M14, 20M12 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 $S\setminus I$. |
| title | On some properties for cofiniteness of submonoids and ideals of an affine semigroup |
| topic | Commutative Algebra 20M14, 20M12 |
| url | https://arxiv.org/abs/2402.05242 |