Results 101 to 110 of about 237,348 (199)
, 1999 We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer.
Haynes, Rhonda S.
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WHEN ARE SYMMETRIC IDEALS MONOMIAL?
Journal of Commutative Algebra, 2023 The notation has been updated and the main result extended; 9 ...
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Strong Persistence Index and Fluctuations in Colon Powers of Monomial Ideals
MathematicsLet I be an ideal in a commutative Noetherian ring R. We say that a positive integer ℓ0 is the strong persistence index of I if ℓ0 is the smallest integer such that (Iℓ+1:RI)=Iℓ for all ℓ≥ℓ0.
Mehrdad Nasernejad, Jonathan T. Toledo
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Monomial Ideals and Planar Graphs [PDF]
, 1999 Grobner basis theory reduces questions about systems of polynomial equations to the combinatorial study of monomial ideals, or staircases. This article gives an elementary introduction to current research in this area. After reviewing the bivariate case, a new correspondence is established between planar graphs and minimal resolutions of monomial ...
Ezra Miller, Bernd Sturmfels
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On Posets, Monomial Ideals, Gorenstein Ideals and their Combinatorics
OrderIn this article we first compare the set of elements in the socle of an ideal of a polynomial algebra $K[x_1,\ldots,x_d]$ over a field $K$ that are not in the ideal itself and Macaulay's inverse systems of such polynomial algebras in a purely combinatorial way for monomial ideals, and then develop some closure operational properties for the related ...
Geir Agnarsson, Neil Epstein
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Monomial ideals with a prescribed Waldschmidt constant [PDF]
Let I be a monomial ideal in R=K[x_1,x_2,..,x_n], a polynomial ring over a field K. The Waldschmidt constant of I is an asymptotic invariant of I. The Waldschmidt constant manifests in many ways in commutative algebra and algebraic geometry, and is ...
Kohne, Craig
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On the weak Lefschetz property of graded modules over K[x, y]
Le Matematiche, 2012 It is known that graded cyclic modules over S = K[x, y] have the Weak Lefschetz Property (WLP). This is not true for non-cyclic modules over S. The purpose of this note is to study which conditions on S-modules ensure the WLP.
Giuseppe Favacchio, Phong Dinh Thieu
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Primary decomposition of monomial ideals
, 2001 Let k be a field and R be a polynomial ring in n variables over k. Every ideal I of R=k[x₁, ... ,x_n]can be written as a finite intersection of primary ideals. A monomial ideal is an ideal of k[x₁, ...
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, 2008 We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus comple-menting Eliahou and Kervaire’s splitting approach.
Adam Van Tuyl +2 more
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The saturation number of monomial ideals [PDF]
, 2023 Let $S=\mathbb{K}[x_1,\ldots, x_n]$ be the polynomial ring over a field $\mathbb{K}$ and $\mathfrak{m}= (x_1, \ldots, x_n)$ be the irredundant maximal ideal of $S$. For an ideal $I \subset S$, let $\mathrm{sat}(I)$ be the minimum number $k$ for which $I \
Pour, Ali Akbar Yazdan +1 more
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