Sayedsadeghi, Mirsadegh and Nasernejad, Mehrdad and Asloob Topaçoğlu, Ayesha
(2022)
*On the embedded associated primes of monomial ideals.*
Rocky Mountain Journal of Mathematics, 52
(1).
pp. 275-287.
ISSN 0035-7596 (Print) 1945-3795 (Online)

Official URL: http://dx.doi.org/10.1216/rmj.2022.52.275

## Abstract

Let I be a square-free monomial ideal in a polynomial ring R = K[x(1),...,x(n)] over a field K, m = (x(1),...,x(n)) be the graded maximal ideal of R, and {u(1),...,u(beta 1(I))} be a maximal independent set of minimal generators of I such that m\x(i) is not an element of Ass(R/(I\x(i))(t)) for all x(i) vertical bar Pi(beta 1(I))(i=1) u(i) and some positive integer t, where I\x(i) denotes the deletion of I at x(i) and beta(1)(I) denotes the maximum cardinality of an independent set in I. We prove that if m is an element of Ass(R/I-t), then t >= beta(1) (I) + 1. As an application, we verify that under certain conditions, every unmixed Konig ideal is normally torsion-free, and so has the strong persistence property. In addition, we show that every square-free transversal polymatroidal ideal is normally torsion-free. Next, we state some results on the corner elements of monomial ideals. In particular, we prove that if I is a monomial ideal in a polynomial ring R = K[x(1),...,x(n)] over a field K and z is an I(t )corner element for some positive integer t such that m\x(i) is not an element of Ass(I\x(i))(t) for some 1 <= i <= n, then x(i) divides z.

Item Type: | Article |
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Uncontrolled Keywords: | associated primes; corner elements; König ideals; normally torsion-free ideals; strong persistence property |

Subjects: | Q Science > QA Mathematics > QA150-272.5 Algebra |

Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |

Depositing User: | Ayesha Asloob Topaçoğlu |

Date Deposited: | 23 Jun 2022 14:25 |

Last Modified: | 22 Aug 2022 15:00 |

URI: | https://research.sabanciuniv.edu/id/eprint/42837 |