On the second powers of Stanley-Reisner ideals

DOI10.1216/JCA-2011-3-3-405zbMath1237.13045arXiv1203.1969MaRDI QIDQ412553

Giancarlo Rinaldo, Naoki Terai, Ken-ichi Yoshida

Publication date: 4 May 2012

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

Full work available at URL: https://arxiv.org/abs/1203.1969

zbMATH Keywords

Cohen-Macaulay ringGorenstein ringsymbolic powerlinkageStanley-Reisner idealBuchsbaum ringcomplete intersection ringcross polytope

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55)

Related Items

On the Cohen-Macaulayness of the conormal module of an ideal ⋮ Buchsbaumness of the second powers of edge ideals ⋮ GORENSTEIN AND S_r PATH IDEALS OF CYCLES ⋮ Combinatorial characterizations of the Cohen-Macaulayness of the second power of edge ideals ⋮ On the associated primes and the depth of the second power of squarefree monomial ideals ⋮ Decreasing behavior of the depth functions of edge ideals ⋮ Licci squarefree monomial ideals generated in degree two or with deviation two ⋮ Cohen-Macaulayness of large powers of Stanley-Reisner ideals ⋮ Simplicial complexes satisfying Serre's condition: a survey with some new results ⋮ Cohen-Macaulayness of saturation of the second power of edge ideals ⋮ Depth and regularity of monomial ideals via polarization and combinatorial optimization ⋮ Saturation and associated primes of powers of edge ideals ⋮ 4-dimensional licci Gorenstein Stanley-Reisner ideals ⋮ Cohen–Macaulayness and Limit Behavior of Depth for Powers of Cover Ideals ⋮ Cohen–Macaulay graphs with large girth ⋮ A characterization of triangle-free Gorenstein graphs and Cohen-Macaulayness of second powers of edge ideals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals
• Cohen-Macaulayness of large powers of Stanley-Reisner ideals
• The Buchsbaum property of symbolic powers of Stanley-Reisner ideals of dimension 1
• Cohen-Macaulayness of powers of two-dimensional squarefree monomial ideals
• \(H\)-vectors of simplicial complexes with Serre's conditions
• Vollständige Durchschnitte in Cohen-Macaulay-Ringen
• On the ideal theory of graphs
• Certain complexes associated to a sequence and a matrix
• Combinatorics and commutative algebra.
• Locally complete intersection Stanley-Reisner ideals
• Cohen-Macaulayness for symbolic power ideals of edge ideals
• Existence of fractional differential equations
• On the radical of a monomial ideal
• Effective Cowsik–Nori Theorem for Edge Ideals
• Über vollständige Durchschnitte in lokalen Ringen
• Deformation and Linkage of Gorenstein Algebras
• Standard graded vertex cover algebras, cycles and leaves
• Multiplicative Structure on Resolutions of Algebras Defined by Herzog Ideals
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
• Linkage and the Koszul Homology of Ideals
• Symbolic powers and matroids
• Cohen-Macaulay edge ideal whose height is half of the number of vertices
• A Note on Gorenstein Rings of Embedding Codimension Three