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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
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
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
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
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
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
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
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
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
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
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
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
Journal Article
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
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 1/2007, Volume 56, Issue 3, pp. 1463 - 1477
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
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
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
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
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 06/2012, Volume 23, Issue 6, pp. 1250065 - 1250038
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
Journal Article
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