On the associated primes and the depth of the second power of squarefree monomial ideals

DOI10.1016/j.jpaa.2013.11.008zbMath1284.13030arXiv1310.5303OpenAlexW2088737132MaRDI QIDQ393525

Naoki Terai, Ngô Viêt Trung

Publication date: 23 January 2014

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.5303

zbMATH Keywords

hypergraphdepthedge idealassociated primecover ideal

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Structure, classification theorems for modules and ideals in commutative rings (13C05) Local cohomology and commutative rings (13D45) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Combinatorial aspects of commutative algebra (05E40)

Related Items

Depth and regularity of powers of sums of ideals ⋮ Irreducible decomposition of powers of edge ideals ⋮ Decreasing behavior of the depth functions of edge ideals ⋮ Regular sequences on squares of monomial ideals ⋮ Depth of Powers of Squarefree Monomial Ideals (Research) ⋮ Unnamed Item ⋮ Saturation and associated primes of powers of edge ideals ⋮ Combinatorial characterizations of the saturation and the associated primes of the fourth power of edge ideals ⋮ Associated primes of powers of edge ideals and ear decompositions of graphs ⋮ Critical paired dominating sets and irreducible decompositions of powers of edge ideals ⋮ Depth functions of symbolic powers of homogeneous ideals ⋮ Squarefree monomial ideals that fail the persistence property and non-increasing depth

Cites Work

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• A conjecture on critical graphs and connections to the persistence of associated primes
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• Embedded associated primes of powers of square-free monomial ideals
• Bounding the socles of powers of squarefree monomial ideals

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