Prime filtrations of monomial ideals and polarizations

DOI10.1016/j.jalgebra.2006.11.002zbMath1142.13022arXivmath/0605119OpenAlexW2073407512MaRDI QIDQ2370261

Ali Soleyman Jahan

Publication date: 22 June 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605119

zbMATH Keywords

prime filtrationsStanley decompositionsmulticomplexespretty clean modules

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55)

Related Items (32)

Upper Bounds for the Stanley Depth ⋮ On a Conjecture of Stanley Depth of Squarefree Veronese Ideals ⋮ Monomial Ideals of Forest Type ⋮ Stanley-Reisner Rings ⋮ A procedure to compute prime filtration ⋮ On Characteristic Poset and Stanley Decomposition of S/I ⋮ Depth and Stanley Depth of Multigraded Modules ⋮ Support posets of some monomial ideals ⋮ Stanley depth of multigraded modules ⋮ How to compute the Stanley depth of a monomial ideal ⋮ Polarization and depolarization of monomial ideals with application to multi-state system reliability ⋮ Very well-covered graphs by Betti splittings ⋮ Spheres arising from multicomplexes ⋮ Linear balls and the multiplicity conjecture ⋮ Block Stanley decompositions. II: Greedy algorithms, applications, and open problems ⋮ Minimal depth of monomial ideals via associated radical ideals ⋮ Stanley decompositions and partitionable simplicial complexes ⋮ Stanley conjecture in small embedding dimension ⋮ Block Stanley decompositions. I: Elementary and gnomon decompositions ⋮ Stanley decompositions in localized polynomial rings ⋮ Interval partitions and Stanley depth ⋮ Computing the Stanley depth ⋮ Stanley depth of monomial ideals with small number of generators ⋮ The stable property of projective dimension ⋮ Prime Filtrations and Primary Decompositions of Modules ⋮ Constructible Ideals ⋮ Cleanness of Cohen-Macaulay monomial ideal generated by at most five elements ⋮ Normality of cover ideals of graphs and normality under some operations ⋮ Prime filtrations and Stanley decompositions of squarefree modules and Alexander duality ⋮ Stanley decompositions and polarization ⋮ Pretty cleanness and filter-regular sequences ⋮ Simplicial complexes of Whisker type

Cites Work

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• Finite filtrations of modules and shellable multicomplexes
• Linear Diophantine equations and local cohomology
• A new algebraic criterion for shellability
• Standard pairs and group relaxations in integer programming
• Bounds on degrees of projective schemes
• Uniform bounds on multigraded regularity
• Combinatorics and commutative algebra

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