Squarefree monomial ideals that fail the persistence property and non-increasing depth

DOI10.1007/s40306-014-0104-xzbMath1320.13015arXiv1405.6809OpenAlexW1996537000MaRDI QIDQ2352390

Mengyao Sun, Huy Tái Hà

Publication date: 1 July 2015

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.6809

zbMATH Keywords

persistenceassociated primescritical graphsmonomial idealssquarefree monomial idealscover idealsnon-increasing depth

Mathematics Subject Classification ID

Trees (05C05) Paths and cycles (05C38) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Polynomials, factorization in commutative rings (13P05) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (10)

Depth and regularity of powers of sums of ideals ⋮ Depth Functions and Symbolic Depth Functions of Homogeneous Ideals ⋮ Depth and regularity modulo a principal ideal ⋮ Decreasing behavior of the depth functions of edge ideals ⋮ Depth of Powers of Squarefree Monomial Ideals (Research) ⋮ A family of monomial ideals with the persistence property ⋮ 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 ⋮ Tensor-multinomial sums of ideals: Primary decompositions and persistence of associated primes ⋮ Depth functions of powers of homogeneous ideals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Squarefree monomial ideals with constant depth function
• On the associated primes and the depth of the second power of squarefree monomial ideals
• Persistence and stability properties of powers of ideals
• Associated primes of monomial ideals and odd holes in graphs
• Progress in commutative algebra 1. Combinatorics and homology
• Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals
• A conjecture on critical graphs and connections to the persistence of associated primes
• The stable set of associated prime ideals of a polymatroidal ideal
• Associated primes of powers of edge ideals
• Monomial ideals whose depth function has any given number of strict local maxima
• Replication in critical graphs and the persistence of monomial ideals
• The depth of powers of an ideal
• Embedded associated primes of powers of square-free monomial ideals
• Asymptotic Stability of Ass(M/I n M)
• The asymptotic nature of the analytic spread
• Monomial Ideals
• Depths of Powers of the Edge Ideal of a Tree

This page was built for publication: Squarefree monomial ideals that fail the persistence property and non-increasing depth