Saturation and associated primes of powers of edge ideals
نویسندگان
چکیده
منابع مشابه
Embedded Associated Primes of Powers of Square-free Monomial Ideals
An ideal I in a Noetherian ringR is normally torsion-free if Ass(R/I) = Ass(R/I) for all t ≥ 1. We develop a technique to inductively study normally torsion-free square-free monomial ideals. In particular, we show that if a squarefree monomial ideal I is minimally not normally torsion-free then the least power t such that I has embedded primes is bigger than β1, where β1 is the monomial grade o...
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Let H denote a finite simple hypergraph. The cover ideal of H, denoted by J = J(H), is the monomial ideal whose minimal generators correspond to the minimal vertex covers of H. We give an algebraic method for determining the chromatic number of H, proving that it is equivalent to a monomial ideal membership problem involving powers of J . Furthermore, we study the sets Ass(R/Js) by exploring th...
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A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$, denoted by match$(G)$. In this paper, we provide a generalization of this result for powers of edge ideals. More precisely, we show that for every graph $G$ and every $sgeq 1$, $${rm reg}( R/ I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2015
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.05.003