Embedded associated primes of powers of square-free monomial 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...
متن کاملStability of Associated Primes of Monomial Ideals*
Let I be a monomial ideal of a polynomial ring R. In this paper we determine a number B such that Ass (I/I) = Ass (I/I) for all n ≥ B. 2000 Mathematics Subject Classification: 13A15, 13D45
متن کاملAsymptotic behaviour of associated primes of monomial ideals with combinatorial applications
Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. We say that $I$ satisfies the persistence property if $mathrm{Ass}_R(R/I^k)subseteq mathrm{Ass}_R(R/I^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{Ass}_R(R/I)$ denotes the set of associated prime ideals of $I$. In this paper, we introduce a class of square-free monomial ideals in the polynomial ring $R=K[x_1,ld...
متن کاملColorings of Hypergraphs, Perfect Graphs, and Associated Primes of Powers of Monomial Ideals
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...
متن کاملAssociated primes of monomial ideals and odd holes in graphs
Let G be a finite simple graph with edge ideal I (G). Let I (G)∨ denote the Alexander dual of I (G). We show that a description of all induced cycles of odd length in G is encoded in the associated primes of (I (G)∨)2. This result forms the basis for a method to detect odd induced cycles of a graph via ideal operations, e.g., intersections, products and colon operations. Moreover, we get a simp...
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 Pure and Applied Algebra
سال: 2010
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2009.05.002