Betti numbers and almost complete intersection monomial ideals
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909622198075392 |
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| author | Mafi, Amir Qadir, Rando Rasul |
| author_facet | Mafi, Amir Qadir, Rando Rasul |
| contents | Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $I$ be a monomial ideal of $R$. In this paper, we present an explicit formula for the Betti numbers of almost complete intersection monomial ideals, which enables a rapid construction of their minimal free resolutions. In addition, we characterize the Cohen-Macaulayness of these ideals and also we show the same result for dominant monomial ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Betti numbers and almost complete intersection monomial ideals Mafi, Amir Qadir, Rando Rasul Commutative Algebra Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $I$ be a monomial ideal of $R$. In this paper, we present an explicit formula for the Betti numbers of almost complete intersection monomial ideals, which enables a rapid construction of their minimal free resolutions. In addition, we characterize the Cohen-Macaulayness of these ideals and also we show the same result for dominant monomial ideals. |
| title | Betti numbers and almost complete intersection monomial ideals |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2505.18788 |