On the arithmetical rank of monomial ideals

DOI10.1016/0021-8693(88)90133-0zbMath0639.13015OpenAlexW2074447092MaRDI QIDQ1100241

Gennady Lyubeznik

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0021-8693(88)90133-0

zbMATH Keywords

monomial idealsminimal prime idealsarithmetical ranknumber of generators of idealsymbolic Rees algebras

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items (34)

ARITHMETICAL RANK OF THE CYCLIC AND BICYCLIC GRAPHS ⋮ Stanley depth and Stanley support-regularity of monomial ideals ⋮ New Classes of Set-theoretic Complete Intersection Monomial Ideals ⋮ Stanley-Reisner Rings ⋮ Symbolic Rees Algebras ⋮ Arithmetical Ranks of Stanley–Reisner Ideals Via Linear Algebra ⋮ On set-theoretic intersections and connectedness of algebraic varieties in \(\mathbb P^n\) ⋮ Monomiale Ideale und mengentheoretische vollständige Durchschnitte. (Monomial ideals and set theoretical complete intersections) ⋮ Symbolic powers of monomial ideals and vertex cover algebras ⋮ Stanley depths of certain Stanley-Reisner rings ⋮ Bounds on the Stanley depth and Stanley regularity of edge ideals of clutters ⋮ Expected resurgence of ideals defining Gorenstein rings ⋮ ON THE STANLEY DEPTH AND SIZE OF MONOMIAL IDEALS ⋮ Koszulness, Krull dimension, and other properties of graph-related algebras ⋮ Symbolic powers of edge ideals of graphs ⋮ Symbolic powers of edge ideals. ⋮ Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs ⋮ Simplicial complexes satisfying Serre's condition: a survey with some new results ⋮ Minimal depth of monomial ideals via associated radical ideals ⋮ A vanishing theorem for local cohomology modules ⋮ On resurgence via asymptotic resurgence ⋮ SYMBOLIC ANALYTIC SPREAD: UPPER BOUNDS AND APPLICATIONS ⋮ Regularity, depth and arithmetic rank of bipartite edge ideals ⋮ Castelnuovo-Mumford regularity and projective dimension of a squarefree monomial ideal ⋮ Local Cohomology at Monomial Ideals inR-Sequences ⋮ Regularity and Koszul property of symbolic powers of monomial ideals ⋮ Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems ⋮ Implosive graphs: Square-free monomials on symbolic Rees algebras ⋮ Cohen–Macaulayness and Limit Behavior of Depth for Powers of Cover Ideals ⋮ Stanley depth and size of a monomial ideal ⋮ Graph and depth of a monomial squarefree ideal ⋮ The Stanley Conjecture on Intersections of Four Monomial Prime Ideals ⋮ On regularity of symbolic Rees algebras and symbolic powers of vertex cover ideals of graphs ⋮ Projective dimension and Castelnuovo–Mumford regularity of t-spread ideals

Cites Work

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• On the finite generation of symbolic blow-ups
• Note on set-theoretic intersections of subvarieties of projective space
• Some Algebraic Sets of High Local Cohomological Dimension in Projective Space
• A Prime Ideal in a Polynomial Ring Whose Symbolic Blow-up is Not Noetherian
• Über lokale Kohomologiegruppen hoher Ordnung.
• On set-theoretic intersections
• On set-theoretic intersections

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