Journal of Algebra, ISSN 0021-8693, 12/2017, Volume 492, pp. 498 - 523

For a pair , where is finitely generated graded module over a standard graded ring of dimension , and is a graded ideal with and generated by elements of the...

Hilbert–Kunz multiplicity | Hilbert–Kunz density | Hilbert–Samuel polynomial | MATHEMATICS | Hilbert-Samuel polynomial | Hilbert-Kunz density | Hilbert-Kunz multiplicity

Hilbert–Kunz multiplicity | Hilbert–Kunz density | Hilbert–Samuel polynomial | MATHEMATICS | Hilbert-Samuel polynomial | Hilbert-Kunz density | Hilbert-Kunz multiplicity

Journal Article

Journal of Algebra, ISSN 0021-8693, 04/2019, Volume 523, pp. 285 - 310

Lower bounds on Hilbert–Samuel multiplicity are known for several types of commutative noetherian local rings, and rings with multiplicities which achieve...

Commutative algebra | Ext-algebras | Yoneda algebras | Koszul algebras | AS-regular algebras | Hilbert–Samuel multiplicity | Minimal multiplicity | Gorenstein algebras | Noncommutative algebra | Hilbert-Samuel multiplicity | LOCAL-RINGS | MATHEMATICS | ALGEBRAS | MODULES

Commutative algebra | Ext-algebras | Yoneda algebras | Koszul algebras | AS-regular algebras | Hilbert–Samuel multiplicity | Minimal multiplicity | Gorenstein algebras | Noncommutative algebra | Hilbert-Samuel multiplicity | LOCAL-RINGS | MATHEMATICS | ALGEBRAS | MODULES

Journal Article

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, ISSN 0020-7721, 03/2014, Volume 45, Issue 3, pp. 4549 - 4558

A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom(R)(C, C) congruent to R and Ext(R)(i) (C, C) = 0 for all i >= 1. For...

OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Canonical modules | Hilbert-Samuel multiplicities | DIMENSION | COMPLEXES | Fat point schemes | Monomial ideals | COMPUTER SCIENCE, THEORY & METHODS | Dualizing modules | Semidualizing modules | AUTOMATION & CONTROL SYSTEMS | Betti numbers

OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Canonical modules | Hilbert-Samuel multiplicities | DIMENSION | COMPLEXES | Fat point schemes | Monomial ideals | COMPUTER SCIENCE, THEORY & METHODS | Dualizing modules | Semidualizing modules | AUTOMATION & CONTROL SYSTEMS | Betti numbers

Journal Article

Communications in Algebra, ISSN 0092-7872, 12/2013, Volume 41, Issue 12, pp. 4549 - 4558

A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom R (C, C) ≅ R and for all i ≥ 1. For certain local Cohen-Macaulay...

Canonical modules | Hilbert-Samuel multiplicities | Fat point schemes | Monomial ideals | Dualizing modules | Semidualizing modules | Betti numbers | MATHEMATICS | DIMENSION | COMPLEXES | IDEALS | Algebra

Canonical modules | Hilbert-Samuel multiplicities | Fat point schemes | Monomial ideals | Dualizing modules | Semidualizing modules | Betti numbers | MATHEMATICS | DIMENSION | COMPLEXES | IDEALS | Algebra

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 01/2020, Volume 96, pp. 108 - 121

In this paper, we present an algorithm for computing the minimal reductions of -primary ideals of Cohen–Macaulay local rings. Using this algorithm, we are able...

Formal power series ring | Hilbert–Samuel multiplicity | Integral closure | Information science | Algorithms

Formal power series ring | Hilbert–Samuel multiplicity | Integral closure | Information science | Algorithms

Journal Article

Journal of Algebra, ISSN 0021-8693, 09/2018, Volume 509, pp. 212 - 239

We define a function, called -multiplicity, that interpolates between Hilbert–Samuel multiplicity and Hilbert–Kunz multiplicity by comparing powers of ideals...

Commutative algebra | Interpolation | Hilbert–Kunz multiplicity | Positive characteristic | Hilbert–Samuel multiplicity | MATHEMATICS | Hilbert-Samuel multiplicity | Hilbert-Kunz multiplicity

Commutative algebra | Interpolation | Hilbert–Kunz multiplicity | Positive characteristic | Hilbert–Samuel multiplicity | MATHEMATICS | Hilbert-Samuel multiplicity | Hilbert-Kunz multiplicity

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2019, Volume 47, Issue 8, pp. 3250 - 3263

The associated Buchsbaum-Rim multiplicities of a module are a descending sequence of non-negative integers. These invariants of a module are a generalization...

Primary 13H15 | Hilbert-Samuel multiplicity | Buchsbaum-Rim function | Secondary 13P99 | cyclic modules | Buchsbaum-Rim multiplicity | Buchsbaum–Rim function | Buchsbaum–Rim multiplicity | Hilbert–Samuel multiplicity | MATHEMATICS | Integers | Modules

Primary 13H15 | Hilbert-Samuel multiplicity | Buchsbaum-Rim function | Secondary 13P99 | cyclic modules | Buchsbaum-Rim multiplicity | Buchsbaum–Rim function | Buchsbaum–Rim multiplicity | Hilbert–Samuel multiplicity | MATHEMATICS | Integers | Modules

Journal Article

Journal of Algebra, ISSN 0021-8693, 2008, Volume 319, Issue 11, pp. 4413 - 4425

We study the Buchsbaum–Rim multiplicity of a finitely generated module over a regular local ring of dimension 2 with maximal ideal . The module under...

Reduction of ideals and modules | Buchsbaum–Rim multiplicity | Linkage | Hilbert–Samuel multiplicity | Hilbert-Samuel multiplicity | Buchsbaum-Rim multiplicity | MATHEMATICS | reduction of ideals and modules | CODIMENSION | MODULES | REDUCTION | RINGS | linkage

Reduction of ideals and modules | Buchsbaum–Rim multiplicity | Linkage | Hilbert–Samuel multiplicity | Hilbert-Samuel multiplicity | Buchsbaum-Rim multiplicity | MATHEMATICS | reduction of ideals and modules | CODIMENSION | MODULES | REDUCTION | RINGS | linkage

Journal Article

Annali dell'Universita di Ferrara, ISSN 0430-3202, 05/2017, Volume 63, Issue 1, pp. 147 - 158

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s11565-016-0250-2

Buchsbaum–Rim multiplicity | Hilbert–Samuel polynomials | Intersection theory | Algebra | Projection

Buchsbaum–Rim multiplicity | Hilbert–Samuel polynomials | Intersection theory | Algebra | Projection

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2012, Volume 229, Issue 1, pp. 633 - 667

We study Hilbert–Samuel multiplicity for points of Schubert varieties in the complete flag variety, by Gröbner degenerations of the Kazhdan–Lusztig ideal. In...

Gröbner basis | Schubert varieties | Hilbert–Samuel multiplicities | Hilbert-Samuel multiplicities | 14N15 | 14M15 | Grobner basis | POLYNOMIALS | MATHEMATICS | GRASSMANNIANS | COMPLEXES | GROBNER GEOMETRY | HILBERT-FUNCTIONS | POINTS | COXETER GROUPS

Gröbner basis | Schubert varieties | Hilbert–Samuel multiplicities | Hilbert-Samuel multiplicities | 14N15 | 14M15 | Grobner basis | POLYNOMIALS | MATHEMATICS | GRASSMANNIANS | COMPLEXES | GROBNER GEOMETRY | HILBERT-FUNCTIONS | POINTS | COXETER GROUPS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2015, Volume 143, Issue 1, pp. 121 - 128

We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-Soderberg theory to obtain...

Gorenstein rings | Hilbert-Samuel multiplicity | Graded Betti numbers | BETTI-NUMBERS | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | graded Betti numbers | PURE

Gorenstein rings | Hilbert-Samuel multiplicity | Graded Betti numbers | BETTI-NUMBERS | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | graded Betti numbers | PURE

Journal Article

Advances in Mathematics, ISSN 0001-8708, 12/2017, Volume 322, pp. 940 - 970

Let be a flat local extension of local rings. Lech conjectured around 1960 that there should be a general inequality on the Hilbert–Samuel multiplicities ....

Hilbert–Kunz multiplicity | Lech's conjecture | Hilbert–Samuel multiplicity | HOMOMORPHISMS | INEQUALITIES | Hilbert-Samuel multiplicity | LOCAL-RINGS | Hilbert-Kunz multiplicity | IDEALS | COUPLES | MATHEMATICS | MODULES | CHOW GROUPS | INTERSECTION MULTIPLICITIES | PROJECTIVE DIMENSION

Hilbert–Kunz multiplicity | Lech's conjecture | Hilbert–Samuel multiplicity | HOMOMORPHISMS | INEQUALITIES | Hilbert-Samuel multiplicity | LOCAL-RINGS | Hilbert-Kunz multiplicity | IDEALS | COUPLES | MATHEMATICS | MODULES | CHOW GROUPS | INTERSECTION MULTIPLICITIES | PROJECTIVE DIMENSION

Journal Article

13.
Full Text
Lech's inequality, the Stückrad–Vogel conjecture, and uniform behavior of Koszul homology

Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 442 - 472

Let be a Noetherian local ring, and let be a finitely generated -module of dimension . We prove that the set is bounded below by where . Moreover, when is...

Hilbert-Samuel multiplicities | Lech's inequality | Stückrad–Vogel conjecture | Koszul homology | MATHEMATICS | Stuckrad-Vogel conjecture | BOUNDS | Equality

Hilbert-Samuel multiplicities | Lech's inequality | Stückrad–Vogel conjecture | Koszul homology | MATHEMATICS | Stuckrad-Vogel conjecture | BOUNDS | Equality

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2007, Volume 56, Issue 3, pp. 1463 - 1477

For commuting tuples R ∈ L(Z)n of Banach-space operators that arise as quotients of lower semi-Fredholm systems T with constant cohomology dimension dim...

Algebra | Analytic functions | Quotients | Natural numbers | Linear transformations | Polynomials | Mathematical rings | Banach space | Commuting | Multivariable operator theory | Hilbert-samuel multiplicity | Stabilized cohomology dimensions | Fredholm tuples | MATHEMATICS | MODULES | INVARIANT | Hilbert-Samuel multiplicity | INDEX | stabilized cohomology dimensions | ANALYTIC-FUNCTIONS | multivariable operator theory

Algebra | Analytic functions | Quotients | Natural numbers | Linear transformations | Polynomials | Mathematical rings | Banach space | Commuting | Multivariable operator theory | Hilbert-samuel multiplicity | Stabilized cohomology dimensions | Fredholm tuples | MATHEMATICS | MODULES | INVARIANT | Hilbert-Samuel multiplicity | INDEX | stabilized cohomology dimensions | ANALYTIC-FUNCTIONS | multivariable operator theory

Journal Article

Tokyo Journal of Mathematics, ISSN 0387-3870, 2010, Volume 33, Issue 2, pp. 341 - 360

Let S be a finitely generated standard multigraded algebra over an Artinian local ring A; M a finitely generated multigraded S-module. This paper first...

Hilbert-Samuel polynomial | Multigraded module | Multiplicity | Artinian ring | MATHEMATICS | 13E10 | 13H15 | 13E05 | 13A02 | 14C17

Hilbert-Samuel polynomial | Multigraded module | Multiplicity | Artinian ring | MATHEMATICS | 13E10 | 13H15 | 13E05 | 13A02 | 14C17

Journal Article

Communications in Algebra, ISSN 0092-7872, 07/2015, Volume 43, Issue 7, pp. 2763 - 2784

Let R be a Cohen-Macaulay local ring with a canonical module ω R . Let I be an -primary ideal of R and M, a maximal Cohen-Macaulay R-module. We call the...

Hilbert-Samuel polynomial | Reduction | Primary 13D40 | Multiplicity | Secondary 13A30 | Hilbert–Samuel polynomial | MATHEMATICS

Hilbert-Samuel polynomial | Reduction | Primary 13D40 | Multiplicity | Secondary 13A30 | Hilbert–Samuel polynomial | MATHEMATICS

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 01/2016, Volume 220, Issue 1, pp. 223 - 245

We study the Łojasiewicz exponent and the log canonical threshold of ideals of when restricted to generic subspaces of of different dimensions. We obtain...

MILNOR NUMBER | NEWTON FILTRATIONS | MATHEMATICS | MATHEMATICS, APPLIED | HYPERSURFACE SINGULARITIES | SECTIONS | MULTIPLIER IDEALS | JOINT REDUCTIONS | MONOMIAL IDEALS

MILNOR NUMBER | NEWTON FILTRATIONS | MATHEMATICS | MATHEMATICS, APPLIED | HYPERSURFACE SINGULARITIES | SECTIONS | MULTIPLIER IDEALS | JOINT REDUCTIONS | MONOMIAL IDEALS

Journal Article

Journal of Commutative Algebra, ISSN 1939-0807, 2018, Volume 10, Issue 3, pp. 393 - 410

Let (R,m) be an unmixed Noetherian local ring, Q a parameter ideal and K an m-primary ideal of R containing Q. We give a necessary and sufficient condition for...

Hilbert-Samuel Polynomial | Cohen- Macaulay ring | Hilbert coefficients | Superficial element | MATHEMATICS | MULTIPLICITY | Cohen-Macaulay ring | CHERN COEFFICIENTS | superficial element | LOCAL-RINGS | FILTRATIONS

Hilbert-Samuel Polynomial | Cohen- Macaulay ring | Hilbert coefficients | Superficial element | MATHEMATICS | MULTIPLICITY | Cohen-Macaulay ring | CHERN COEFFICIENTS | superficial element | LOCAL-RINGS | FILTRATIONS

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 06/2012, Volume 23, Issue 6, pp. 1250065 - 1250038

Let Ω be a bounded hyperconvex domain in ℂn, 0 ∈ Ω, and Sε a family of N poles in Ω, all tending to 0 as ε tends to 0. To each Sε we associate its vanishing...

complex MongeAmpère equation | Pluricomplex Green function | residues | BriançonSkoda theorem | HilbertSamuel multiplicity | ideals of holomorphic functions | analytic disks | SPACES | PLURISUBHARMONIC-FUNCTIONS | Hilbert-Samuel multiplicity | complex Monge-Ampere equation | MATHEMATICS | POLES | MONGE-AMPERE MEASURES | CONVERGENCE | Briancon-Skoda theorem | Poles | Multipoles | Green's functions | Mathematical analysis | Convergence | Complex Variables | Algebraic Geometry | Mathematics

complex MongeAmpère equation | Pluricomplex Green function | residues | BriançonSkoda theorem | HilbertSamuel multiplicity | ideals of holomorphic functions | analytic disks | SPACES | PLURISUBHARMONIC-FUNCTIONS | Hilbert-Samuel multiplicity | complex Monge-Ampere equation | MATHEMATICS | POLES | MONGE-AMPERE MEASURES | CONVERGENCE | Briancon-Skoda theorem | Poles | Multipoles | Green's functions | Mathematical analysis | Convergence | Complex Variables | Algebraic Geometry | Mathematics

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2013, Volume 63, Issue 5, pp. 1793 - 1847

In this paper we study a notion of local volume for Cartier divisors on arbitrary blow-ups of normal complex algebraic varieties of dimension greater than one,...

Plurigenera | Hilbert-Samuel multiplicity | Okounkov body | Asymptotic invariants | Local volumes | MATHEMATICS | ISOLATED SINGULARITIES | asymptotic invariants | GENERAL TYPE | plurigenera | ASYMPTOTIC-BEHAVIOR

Plurigenera | Hilbert-Samuel multiplicity | Okounkov body | Asymptotic invariants | Local volumes | MATHEMATICS | ISOLATED SINGULARITIES | asymptotic invariants | GENERAL TYPE | plurigenera | ASYMPTOTIC-BEHAVIOR

Journal Article

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