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 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...
متن کاملRigid monomial ideals
In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial ideals are lattice-linear and thus their minimal resolution can be constructed as a poset resolution. We then use this result to give a description of the m...
متن کاملPower of Monomial Ideals
1. Preliminaries 3 2. Gröbner Bases 3 2.1. Motivating Problems 3 2.2. Ordering of Monomials 3 2.3. The Division Algorithm in S = k[x1, . . . , xn] 5 2.4. Dickson’s Lemma 7 2.5. Gröbner Bases and the Hilbert Basis Theorem 10 2.6. Some Further Applications of Gröbner bases 18 3. Hilbert Functions 21 3.1. Macaulay’s Theorem 27 3.2. Hilbert Functions of Reduced Standard Graded k-algebras 37 3.3. Hi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2015
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2014.952012