منابع مشابه
Monomial Ideals
Monomial ideals form an important link between commutative algebra and combinatorics. In this chapter, we demonstrate how to implement algorithms in Macaulay 2 for studying and using monomial ideals. We illustrate these methods with examples from combinatorics, integer programming, and algebraic geometry.
متن کاملNew Classes of Set-theoretic Complete Intersection Monomial Ideals
Let ∆ be a simplicial complex and χ be an s-coloring of ∆. Biermann and Van Tuyl have introduced the simplicial complex ∆χ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of ∆χ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of ∆χ over a field is set-theoretic complete interse...
متن کاملMonomial Ideals, Almost Complete Intersections and the Weak Lefschetz Property
has maximal rank, i.e. it is injective or surjective. In this case, the linear form L is called a Lefschetz element of A. (We will often abuse notation and say that the corresponding ideal has the WLP.) The Lefschetz elements of A form a Zariski open, possibly empty, subset of (A)1. Part of the great interest in the WLP stems from the fact that its presence puts severe constraints on the possib...
متن کاملMonomial Ideals and Duality
These are lecture notes, in progress, on monomial ideals. The point of view is that monomial ideals are best understood by drawing them and looking at their corners, and that a combinatorial duality satisfied by these corners, Alexander duality, is key to understanding the more algebraic duality theories at play in algebraic geometry and commutative algebra. Sections written so far cover Alexan...
متن کاملSplittings of Monomial Ideals
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 complementing Eliahou and Kervaire’s splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay bi...
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ژورنال
عنوان ژورنال: Journal of Commutative Algebra
سال: 2016
ISSN: 1939-2346
DOI: 10.1216/jca-2016-8-2-207