Results 1 to 10 of about 177 (175)
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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Monomial Ideals under Ideal Operations [PDF]
Communications in Algebra, 2015 In this paper, we show for a monomial ideal $I$ of $K[x_1,x_2,\ldots,x_n]$ that the integral closure $\ol{I}$ is a monomial ideal of Borel type (Borel-fixed, strongly stable, lexsegment, or universal lexsegment respectively), if $I$ has the same property.
Guo, Jin, Wu, Tongsuo
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Some counterexamples for (strong) persistence property and (nearly) normally torsion-freeness
Examples and Counterexamples, 2023 In this article, we present some rare counterexamples, which are related to (strong) persistence property and (nearly) normally torsion-freeness of monomial ideals.
Mehrdad Nasernejad
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Monomial s-sequences arising from graph ideals
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2023 Ideals arising from graphs are investigated via s-sequence theory. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of an acyclic graph G is considered for describing the Groebner basis of the relation ideal J of the ...
Maurizio Imbesi, Monica La Barbiera
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Klyachko Diagrams of Monomial Ideals
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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Monomial difference ideals [PDF]
Proceedings of the American Mathematical Society, 2016 In this paper, basic properties of monomial difference ideals are studied. We prove the finitely generated property of well-mixed difference ideals generated by monomials. Furthermore, a finite prime decomposition of radical well-mixed monomial difference ideals is given.
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Communications, 2014 The paper deals with the problem of the expression of associated prime ideals of monomial curves in the affine space A4 as set-theoretic complete intersections.
Michaela Holesova
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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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Steiner Configurations Ideals: Containment and Colouring
Mathematics, 2021 Given a homogeneous ideal I⊆k[x0,…,xn], the Containment problem studies the relation between symbolic and regular powers of I, that is, it asks for which pairs m,r∈N, I(m)⊆Ir holds.
Edoardo Ballico +4 more
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