On the embedded associated primes of monomial ideals

Sayedsadeghi, Mirsadegh; Nasernejad, Mehrdad; Qureshi, Ayesha Asloob

doi:10.1216/rmj.2022.52.275

Cited by 8 publications

(7 citation statements)

References 23 publications

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“…We can finally deduce from [22,Proposition 4.3.29] that I \ x j is normally torsion-free. The last assertion can be deduced from [19,Corollary 3.5], and the proof is over.…”

Section: Some Results On the Embedded Associated Primesmentioning

confidence: 82%

“…. , s. Thanks to L is a square-free monomial ideal, one can deduce from [19,Proposition 4.8] that θ ≤ s −1.…”

Section: Some Results On the Embedded Associated Primesmentioning

confidence: 99%

“…Assume that p ∈ Ass(L s , h). Since L s + hR = (I ∩ q) s + hR, It follows immediately from [19,Theorem 3.3] that q ′ ∈ Ass(I ∩ q) s . Due to I ∩ q is normally torsion-free, this gives that q ′ ∈ Min(I ∩ q).…”

Section: Preliminariesmentioning

confidence: 99%

“…Let p ∈ Ass((L s : h ℓ−1 ), h). Thanks to ((L s : h ℓ−1 ), h) = I ℓ−1 (I ∩ q) s−ℓ+1 + hR, [19,Theorem 3.3] implies that q ′ ∈ Ass(I ℓ−1 (I ∩ q) s−ℓ+1 ). According to Proposition 2.2, we can derive that q ′ ∈ Min(I) ∪ {q}.…”

Section: Preliminariesmentioning

confidence: 99%

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Classes of normally and nearly normally torsion-free monomial ideals

Nasernejad

Qureshi

Khashyarmanesh

et al. 2022

Communications in Algebra

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Let I ⊂ R = K[x 1 , . . . , x n ] be a square-free monomial ideal, q be a prime monomial ideal in R, h be a square-free monomial in R with supp(h) ∩ (supp(q) ∪ supp(I)) = ∅, and L := I ∩ (q, h). In this paper, we first focus on the associated primes of powers of L and explore the normally torsion-freeness of L. We also give an application on a combinatorial result. Next, we study when a square-free monomial ideal is minimally not normally torsion-free. Particularly, we introduce a class of square-free monomial ideals, which are minimally not normally torsion-free.

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“…We can finally deduce from [22,Proposition 4.3.29] that I \ x j is normally torsion-free. The last assertion can be deduced from [19,Corollary 3.5], and the proof is over.…”

Section: Some Results On the Embedded Associated Primesmentioning

confidence: 82%

“…. , s. Thanks to L is a square-free monomial ideal, one can deduce from [19,Proposition 4.8] that θ ≤ s −1.…”

Section: Some Results On the Embedded Associated Primesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

See 2 more Smart Citations

Classes of normally and nearly normally torsion-free monomial ideals

Nasernejad

Qureshi

Khashyarmanesh

et al. 2022

Communications in Algebra

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“…Suppose, on the contrary, that m ∈ Ass(L 2 ). This gives that m = (L 2 : v) for some monomial v ∈ R. By virtue of [23,Proposition 4.8], one has deg xi (v) ≤ 1 for all i = 1, . .…”

Section: On the Closed Neighborhood Ideals And Dominating Ideals Of C...mentioning

confidence: 99%

Normality and associated primes of Closed neighborhood ideals and dominating ideals

Nasernejad,

Bandari,

Roberts

2022

Preprint

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In this paper, we first give some criteria for normality of monomial ideals. As applications, we show that closed neighborhood ideals of complete bipartite graphs are normal, and hence satisfy the (strong) persistence property. We also prove that dominating ideals of complete bipartite graphs are nearly normally torsion-free. In addition, we show that dominating ideals of h-wheel graphs, under certain condition, are normal.

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