Results 21 to 30 of about 237,348 (199)
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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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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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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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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Homology and Combinatorics of Monomial Ideals
, 2022 This thesis is in combinatorial commutative algebra. It contains four papers, the first three of which concern homological properties and invariants of monomial ideals.
Orlich, Milo
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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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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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Multiplicities of monomial ideals
Journal of Algebra, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Herzog, Jürgen, Srinivasan, Hema
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Monomial Ideals with Primary Components given by Powers of Monomial Prime Ideals [PDF]
The Electronic Journal of Combinatorics, 2014 We characterize monomial ideals which are intersections of powers of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.
Herzog, Jürgen, Vladoiu, Marius
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