Results 11 to 20 of about 237,348 (199)
On Monomial Golod Ideals [PDF]
Acta Mathematica Vietnamica, 2020 AbstractWe study ideal-theoretic conditions for a monomial ideal to be Golod. For ideals in a polynomial ring in three variables, our criteria give a complete characterization. Over such rings, we show that the product of two monomial ideals is Golod.
Dao H., De Stefani A.
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Normality Criteria for Monomial Ideals [PDF]
Results in Mathematics, 2022 In this paper we study the normality of monomial ideals using linear programming and graph theory. We give normality criteria for monomial ideals, for ideals generated by monomials of degree two, and for edge ideals of graphs and clutters and their ideals of covers.
Luis A. Dupont +2 more
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The graph of monomial ideals [PDF]
Journal of Pure and Applied Algebra, 2005 15 pages ...
Altmann, Klaus, Sturmfels, Bernd
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Antichains of monomial ideals are finite [PDF]
Proceedings of the American Mathematical Society, 2000 The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the literature and new results. One natural generalization to more abstract posets is shown to be false.
Maclagan, Diane
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Tameness of local cohomology of monomial ideals with respect to monomial prime ideals [PDF]
Journal of Pure and Applied Algebra, 2007 In this paper we consider the local cohomology of monomial ideals with respect to monomial prime ideals and show that all these local cohomology modules are tame.
Rahimi, Ahad
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MONOMIAL IDEALS FROM A SEMIRING PERSPECTIVE [PDF]
Tạp chí Khoa học Đại học Đà LạtWe formulate the theory of monomial ideals of a ring of polynomials with coefficients in a field through the theory of semirings. In particular, we focus on the theory of integrally closed monomial ideals.
Cristhian Garay-López +2 more
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Generic and Cogeneric Monomial Ideals [PDF]
Journal of Symbolic Computation, 2000 Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated chain condition, and the Cohen-Macaulay property implies shellability for both the Scarf complex and the Stanley ...
Ezra Miller +2 more
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Superficial ideals for monomial ideals
Journal of Algebra and Its Applications, 2018 Let [Formula: see text] and [Formula: see text] be two ideals in a commutative Noetherian ring [Formula: see text]. We say that [Formula: see text] is a superficial ideal for [Formula: see text] if the following conditions are satisfied: (i) [Formula: see text], where [Formula: see text] denotes a minimal set of generators of an ideal [Formula: see ...
Rajaee, Saeed +2 more
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On properties of monomial ideals and algebras.
, 2022 Monomial ideals form an important link between commutative algebra and combinatorics. Our aim is to study various operations on monomial ideals and algebras, as well as their properties. This thesis consists of an introduction and four research articles. The introduction covers the necessary background and the existing results. The first two papers are
Gasanova, Oleksandra
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