Minimal reductions and cores of edge ideals
نویسندگان
چکیده
منابع مشابه
Binomial edge ideals and rational normal scrolls
Let $X=left( begin{array}{llll} x_1 & ldots & x_{n-1}& x_n\ x_2& ldots & x_n & x_{n+1} end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...
متن کاملMonomial Ideals, Edge Ideals of Hypergraphs, and Their Minimal Graded Free Resolutions
We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The theme of this paper is to understand how the combinatorial structure of a hypergraph H appears within the resolution of its edge ideal I(H). We discuss when recursive formulas to compute the graded Betti numbers of I(H) in terms of its sub...
متن کاملRegularity of second power of edge ideals
Let G be a graph with edge ideal I(G). Benerjee and Nevo proved that for every graph G, the inequality reg(I(G)2)≤reg(I(G))+2 holds. We provide an alternative proof for this result.
متن کاملNoether Normalizations, Reductions of Ideals, and Matroids
We show that given a finitely generated standard graded algebra of dimension d over an infinite field, its graded Noether normalizations obey a certain kind of ‘generic exchange’, allowing one to pass between any two of them in at most d steps. We prove analogous generic exchange theorems for minimal reductions of an ideal, minimal complete reductions of a set of ideals, and minimal complete re...
متن کاملOn t-reductions of ideals in pullbacks
Let R be an integral domain and I a nonzero ideal of R. An ideal J ⊆ I is a t-reduction of I if (JI)t = (I)t for some positive integer n; and I is t-basic if it has no t-reduction other than the trivial ones. This paper investigates t-reductions of ideals in pullback constructions of type . Section 2 examines the correlation between the notions of reduction and t-reduction in pseudo-valuation d...
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: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.03.018