Criteria for the presence of the maximal ideal in the set of associated primes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918517121482752 |
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| author | Nasernejad, Mehrdad Toledo, Jonathan |
| author_facet | Nasernejad, Mehrdad Toledo, Jonathan |
| contents | In this paper, we establish some criteria to detect the presence of the maximal ideal $(x_1, \ldots, x_n)$ in the set of associated primes of powers of monomial ideals in the polynomial ring $K[x_1, \ldots, x_n]$. Furthermore, for each of these criteria, we illustrate its applicability with corresponding examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Criteria for the presence of the maximal ideal in the set of associated primes Nasernejad, Mehrdad Toledo, Jonathan Commutative Algebra In this paper, we establish some criteria to detect the presence of the maximal ideal $(x_1, \ldots, x_n)$ in the set of associated primes of powers of monomial ideals in the polynomial ring $K[x_1, \ldots, x_n]$. Furthermore, for each of these criteria, we illustrate its applicability with corresponding examples. |
| title | Criteria for the presence of the maximal ideal in the set of associated primes |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2510.16566 |