Sequentially Cohen-Macaulay and pretty clean monomial ideals
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916633457459200 |
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| author | Mafi, Amir Qadir, Rando Rasul Saremi, Hero |
| author_facet | Mafi, Amir Qadir, Rando Rasul Saremi, Hero |
| contents | Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be monomial ideal of $R$. In this paper, we show that if $I$ is a generic monomial ideal, then $R/I$ is pretty clean if and only if $R/I$ is sequentially Cohen-Macaulay. Furthermore, we prove that this equivalence remains unchanged for some special monomial ideals. Moreover, we provide an example that disproves the conjecture raised in \cite[p. 123]{S1} regarding generic monomial ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20043 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequentially Cohen-Macaulay and pretty clean monomial ideals Mafi, Amir Qadir, Rando Rasul Saremi, Hero Commutative Algebra Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be monomial ideal of $R$. In this paper, we show that if $I$ is a generic monomial ideal, then $R/I$ is pretty clean if and only if $R/I$ is sequentially Cohen-Macaulay. Furthermore, we prove that this equivalence remains unchanged for some special monomial ideals. Moreover, we provide an example that disproves the conjecture raised in \cite[p. 123]{S1} regarding generic monomial ideals. |
| title | Sequentially Cohen-Macaulay and pretty clean monomial ideals |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2502.20043 |