Results 11 to 20 of about 1,404 (215)

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.
Diane Maclagan
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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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Stanley depth of monomial ideals with small number of generators

Open Mathematics, 2009
Cimpoeaş Mircea
exaly   +2 more sources

On Monomial Ideals and Their Socles [PDF]

Order, 2019
For a finite subset $M\subset [x_1,\ldots,x_d]$ of monomials, we describe how to constructively obtain a monomial ideal $I\subseteq R = K[x_1,\ldots,x_d]$ such that the set of monomials in $\text{Soc}(I)\setminus I$ is precisely $M$, or such that $\overline{M}\subseteq R/I$ is a $K$-basis for the the socle of $R/I$.
Geir Agnarsson, Neil Epstein
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A non-partitionable Cohen–Macaulay simplicial complex [PDF]

Discrete Mathematics & Theoretical Computer Science, 2020
A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex is partition- able. We disprove the conjecture by constructing an explicit counterexample.
Art M. Duval, Bennet Goeckner, Caroline J. Klivans, Jeremy Martin   +3 more
doaj   +1 more source

Bounds for the minimum distance function

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Let I be a homogeneous ideal in a polynomial ring S. In this paper, we extend the study of the asymptotic behavior of the minimum distance function δI of I and give bounds for its stabilization point, rI, when I is an F -pure or a square-free monomial ...
Núñez-Betancourt Luis, Pitones Yuriko, Villarreal Rafael H.   +2 more
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Orderings of monomial ideals [PDF]

Fundamenta Mathematicae, 2004
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set.
Aschenbrenner, Matthias, Pong, Wai Yan
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A note on the multiplier ideals of monomial ideals [PDF]

Czechoslovak Mathematical Journal, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gong, Cheng, Tang, Zhongming
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Multiplier ideals of monomial ideals [PDF]

Transactions of the American Mathematical Society, 2001
In this note we discuss a simple algebraic calculation of the multiplier ideal associated to a monomial ideal in affine n n
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POLYMATROIDAL IDEALS AND LINEAR RESOLUTION [PDF]

Journal of Algebraic Systems
Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and$I\subset S$ be a monomial ideal with a linearresolution. Let$\frak{m}=(x_1,\ldots,x_n)$ be the unique homogeneous maximal ideal and $I\frak{m}$ be apolymatroidal ideal.
Somayeh Bandari
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