Results 11 to 20 of about 887,096 (204)
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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Klyachko Diagrams of Monomial Ideals [PDF]
Algebras and Representation Theory, 2022 AbstractIn this paper, we introduce the notion of a Klyachko diagram for a monomial ideal I in a certain multi-graded polynomial ring, namely the Cox ring R of a smooth complete toric variety, with irrelevant maximal ideal B. We present procedures to compute the Klyachko diagram of I from its monomial generators, and to retrieve the B −saturation Isat ...
Rosa M. Miró-Roig, Marti Salat-Moltó
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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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On the Hilbert series of monomial ideals [PDF]
Journal of Combinatorial Theory, Series A, 2013 AbstractTo every squarefree monomial ideal one can associate a hypergraph. In this paper we show that the Hilbert series of a squarefree monomial ideal can be obtained from the so-called edge induced polynomial of the associated hypergraph.
Goodarzi, Afshin, Goodarzi, Afshin,
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Poincaré series of monomial rings with minimal Taylor resolution [PDF]
Le Matematiche, 2012 We give a comparison between the Poincaré series of two monomial rings: R = A/I and R_q = A/I_q where I_q is a monomial ideal generated by the q’th power of monomial generators of I.
Yohannes Tadesse
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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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Hypersurface singularities with monomial Jacobian ideal [PDF]
, 2021 We show that every convergent power series with monomial extended Jacobian ideal is right equivalent to a Thom-Sebastiani polynomial. This solves a problem posed by Hauser and Schicho.
Epure, Raul, Schulze, Mathias
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Stanley depth of monomial ideals with small number of generators [PDF]
Open Mathematics, 2009 For a monomial ideal $I\subset S=K[x_1,...,x_n]$, we show that $\sdepth(S/I)\geq n-g(I)$, where $g(I)$ is the number of the minimal monomial generators of $I$. If $I=vI'$, where $v\in S$ is a monomial, then we see that $\sdepth(S/I)=\sdepth(S/I')$.
Cimpoeaş Mircea
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ON A CLASS OF MONOMIAL IDEALS [PDF]
Bulletin of the Australian Mathematical Society, 2013 AbstractLet $S$ be a polynomial ring over a field $K$ and let $I$ be a monomial ideal of $S$. We say that $I$ is MHC (that is, $I$ satisfies the maximal height condition for the associated primes of $I$) if there exists a prime ideal $\mathfrak{p}\in {\mathrm{Ass} }_{S} \hspace{0.167em} S/ I$ for which $\mathrm{ht} (\mathfrak{p})$ equals the number of ...
Borna, Keivan, Jafari, Raheleh
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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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