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Journal of Commutative Algebra, ISSN 1939-0807, 2018, Volume 10, Issue 3, pp. 339 - 345
We extend a result of Caviglia and Sbarra to a polynomial ring with base field of any characteristic. Given a homogeneous ideal containing both a piecewise lex... 
Hilbert function | Piecewise lex ideals | Graded Betti numbers | Lex-plus-powers conjecture | MATHEMATICS | lex-plus-powers conjecture | PLUS-POWERS CONJECTURE | piecewise lex ideals | GREEN-HARRIS CONJECTURE
Journal Article
Journal of Symbolic Computation, ISSN 0747-7171, 07/2019, Volume 93, pp. 120 - 132
Consider a polynomial ring in a finite number of variables over a field of characteristic 0. We implement in CoCoA some algorithms in order to easy compute... 
Monomial ideals | Algorithms | Graded ideals | Minimal graded resolution | Extremal Betti numbers | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Communications in Algebra, ISSN 0092-7872, 08/2019, Volume 47, Issue 8, pp. 3123 - 3140
We investigate the standard generalized Gorenstein algebras of homological dimension three, giving a structure theorem for their resolutions. Moreover in many... 
Graded minimal free resolutions | homological dimension | graded Betti numbers | Gorenstein ideals | 13 H 10 | structure theorems | 14 N 20 | 13 D 40 | MATHEMATICS | Homology
Journal Article
Algebra Colloquium, ISSN 1005-3867, 09/2016, Volume 23, Issue 3, pp. 519 - 530
Let K be a field and let S = K[x(1),...,x(n)] be a polynomial ring over K. Let F = circle plus(r)(i-1) Se-i be a finitely generated graded free S-module with... 
minimal graded resolutions | squarefree monomial modules | graded modules | MATHEMATICS | LEXSEGMENT IDEALS | MATHEMATICS, APPLIED
Journal Article
Algebra Colloquium, ISSN 1005-3867, 06/2018, Volume 25, Issue 2, pp. 335 - 348
Journal Article
MATHEMATICS, ISSN 2227-7390, 08/2019, Volume 7, Issue 8, p. 695
Let K be a field and let S=K[x1,MIDLINE HORIZONTAL ELLIPSIS,xn] be a polynomial ring over K. We analyze the extremal Betti numbers of special squarefree... 
MATHEMATICS | squarefree monomial ideals | graded ideals | minimal graded resolutions | t-spread monomial ideals | extremal Betti numbers
Journal Article
Journal of Algebra, ISSN 0021-8693, 07/2014, Volume 410, pp. 244 - 257
We study inequalities between graded Betti numbers of ideals in a standard graded algebra over a field and their images under embedding maps, defined earlier... 
Graded Betti numbers | Hyperplane restriction theorems | Lex-plus-powers conjecture | Embeddings of Hilbert functions | MATHEMATICS | MINIMAL RESOLUTIONS | CLEMENTS-LINDSTROM RINGS | GENERIC FORMS | MONOMIAL IDEALS | SCHEMES | Statistics | Algebra
Journal Article
Journal of Algebra, ISSN 0021-8693, 10/2015, Volume 440, pp. 642 - 667
In this paper we study graded Betti numbers of any nondegenerate 3-regular algebraic set in a projective space . More concretely, via Generic initial ideals... 
Graded Betti numbers | Generic initial ideals | Linear normality | 3-regular scheme | MATHEMATICS | SYZYGIES | INITIAL IDEALS | PROPERTY | VARIETIES | GEOMETRY
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 4/2008, Volume 27, Issue 2, pp. 215 - 245
We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The... 
Graded resolutions | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Monomial ideals | Computer Science, general | Combinatorics | Hypergraphs | Regularity | Chordal graphs | MATHEMATICS | hypergraphs | graded resolutions | RESOLUTIONS | chordal graphs | regularity | monomial ideals
Journal Article
Communications in Algebra, ISSN 0092-7872, 02/2016, Volume 44, Issue 2, pp. 710 - 730
Given a finite simple graph, one can associate the edge ideal. In this article, we prove that a graded Betti number of the edge ideal does not vanish if the... 
Graded Betti numbers | Lyubeznik resolutions | Projective dimension | Edge ideals | Complete bipartite graphs | Primary: 13D02, 13F55 | Secondary: 05C99 | MATHEMATICS | INDEPENDENCE | REGULARITY | BOUNDS | MONOMIAL IDEALS | MINIMAL FREE RESOLUTIONS
Journal Article
Pure and Applied Mathematics Quarterly, ISSN 1558-8599, 2015, Volume 11, Issue 2, pp. 267 - 281
Let K be a field, V a K-vector space with basis e(1),..., en, and E the exterior algebra of V. To a given monomial ideal I not subset of E we associate a... 
Exterior algebra | Monomial ideals | Betti numbers | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | THEOREMS | LENGTH | GRADED IDEALS | HILBERT FUNCTION | monomial ideals
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 03/2015, Volume 219, Issue 3, pp. 591 - 621
We prove in particular that the Gorenstein numerical semigroup ring generated by has a transcendental series of Betti numbers. The methods of proofs are the... 
MATHEMATICS | MATHEMATICS, APPLIED | LOCAL-RINGS | ALGEBRA | IRRATIONAL POINCARE-BETTI | betti numbers | Gorenstein ring | Naturvetenskap | graded Lie algebras | Algebra and Logic | Algebra och logik | Mathematics | Natural Sciences | Matematik
Journal Article
Mathematics, ISSN 2227-7390, 11/2017, Volume 5, Issue 4, p. 56
Let S be a polynomial ring in n variables over a field K of any characteristic. Given a strongly stable submodule M of a finitely generated graded free... 
Monomial modules | Graded modules | Minimal graded resolution | Extremal Betti numbers | MATHEMATICS | graded modules | monomial modules | minimal graded resolution | extremal Betti numbers | Construction standards
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2010, Volume 138, Issue 1, pp. 61 - 73
Journal Article
Algebra and Number Theory, ISSN 1937-0652, 2012, Volume 6, Issue 3, pp. 437 - 454
We use results of Eisenbud and Schreyer to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear... 
Graded modules | Multiplicity conjecture | Betti numbers | MATHEMATICS | GORENSTEIN ALGEBRAS | BOUNDS | RESOLUTIONS | graded modules | PURE | multiplicity conjecture | IDEALS
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2010, Volume 38, Issue 11, pp. 4348 - 4361
Let Q ∈  [x 1 ,..., x n ] = S be a homogeneous polynomial of degree d. The freeness of the logarithmic derivation module, D(Q), and of its natural... 
32S25 | Logarithmic derivation module | 13N15 | Graded Betti numbers | MATHEMATICS | ARRANGEMENT | FORMULA | Derivation | Algebra | Equivalence | Modules
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2009, Volume 37, Issue 11, pp. 4012 - 4025
We introduce the k-strong Lefschetz property and the k-weak Lefschetz property for graded Artinian K-algebras, which are generalizations of the Lefschetz... 
Lefschetz property | Secondary 13D40, 13E10, 13D02 | Primary 13A02 | Generic initial ideal | Almost revlex ideal | Graded Betti number | WEAK | MATHEMATICS | ALGEBRAS | Quotients | Upper bounds | Algebra
Journal Article
Transactions of the Moscow Mathematical Society, ISSN 0077-1554, 2013, Volume 74, pp. 175 - 202
. We also describe connections between the obtained results and the known results of other authors.]]> 
Generalized polyhedral join | Polyhedral join | Graded betti numbers | Simplicial complex operad | Simplicial wedge | Polyhedral product | Polarization of a homogeneous ideal | Enumerating polynomials
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 3/2010, Volume 31, Issue 2, pp. 299 - 318
Let A=K[x 1,…,x n ] be a polynomial ring over a field K and M a monomial ideal of A. The quotient ring R=A/M is said to be Macaulay-Lex if every Hilbert... 
Lex ideals | Colored simplicial complexes | Graded Betti numbers | Convex and Discrete Geometry | Hilbert functions | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | MATHEMATICS | THEOREM | COMPLEXES | HILBERT FUNCTION | Statistics | Universities and colleges
Journal Article
Algebra and Number Theory, ISSN 1937-0652, 2013, Volume 7, Issue 5, pp. 1019 - 1064
We show that there exists a saturated graded ideal in a standard graded polynomial ring which has the largest total Betti numbers among all saturated graded... 
Hilbert polynomials | Graded betti numbers | MATHEMATICS | graded Betti numbers | MINIMAL RESOLUTIONS | DEPTH | IDEALS | Mathematics - Commutative Algebra
Journal Article
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