Squarefree monomial ideals with constant depth function

DOI10.1016/j.jpaa.2012.12.009zbMath1284.13015arXiv1209.5890OpenAlexW2167586703MaRDI QIDQ387402

Marius Vladoiu, Jürgen Herzog

Publication date: 23 December 2013

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

Full work available at URL: https://arxiv.org/abs/1209.5890

zbMATH Keywords

Rees algebrapowers of idealsedge idealsdepth functionsquarefree monomial idealsfacet idealsmatroidal ideals

Mathematics Subject Classification ID

Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Other special types of modules and ideals in commutative rings (13C13) Combinatorial aspects of commutative algebra (05E40) Arithmetic rings and other special commutative rings (13F99)

Related Items (11)

Depth and regularity of powers of sums of ideals ⋮ When does depth stabilize early on? ⋮ On the matroidal path ideals ⋮ A note on stability properties of powers of polymatroidal ideals ⋮ Regular sequences on squares of monomial ideals ⋮ Depth of Powers of Squarefree Monomial Ideals (Research) ⋮ Powers of sums and their homological invariants ⋮ An effective avoidance principle for a class of ideals ⋮ Stability of depth functions of cover ideals of balanced hypergraphs ⋮ On stability properties of powers of polymatroidal ideals ⋮ Squarefree monomial ideals that fail the persistence property and non-increasing depth

Uses Software

• CoCoA

Cites Work

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• The facet ideal of a simplicial complex
• Simplicial complexes with rigid depth
• The stable set of associated prime ideals of a polymatroidal ideal
• Monomial localizations and polymatroidal ideals
• Associated primes of powers of edge ideals
• Monomial ideals whose depth function has any given number of strict local maxima
• The depth of powers of an ideal
• On the radical of a monomial ideal
• Some Arithmetic Properties of Matroidal Ideals
• The asymptotic nature of the analytic spread
• The diagonal subring and the Cohen-Macaulay property of a multigraded ring

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