Associated Primes of the Square of the Alexander Dual of Hypergraphs
نویسنده
چکیده
The purpose of this paper is to provide methods for determining the associated primes of (I(H)) for an m-hypergraph H . We prove a general method for detecting associated primes of the square of the Alexander dual of the edge ideal based on combinatorial conditions on the m-hypergraph. Also, we demonstrate a more efficient combinatorial criterion for detecting the non-existence of non-minimal associated primes. In investigating 3-hypergraphs, we prove a surprising extension of the previously discovered results for 2-hypergraphs (simple graphs). For 2-hypergraphs, associated primes of the square of the Alexander dual of the edge ideal are either of height 2 or of odd height greater than 2. However, we prove that in the 3-hypergraph case, there is no such restriction or indeed any restriction on the heights of the associated primes. Further, we generalize this result to any dimension greater than 3. Specifically, given any integers m, q, and n with 3 ≤ m ≤ q ≤ n, we construct a m-hypergraph of size n with an associated prime of height q. We further prove that it is possible to construct connected m-hypergraphs under the same conditions.
منابع مشابه
Asymptotic 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 کاملOn the Associated Primes of the generalized $d$-Local Cohomology Modules
The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary generalized local cohomology modules. Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$ are finitely generated $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...
متن کاملMental Representation of Cognates/Noncognates in Persian-Speaking EFL Learners
The purpose of this study was to investigate the mental representation of cognate and noncognate translation pairs in languages with different scripts to test the prediction of dual lexicon model (Gollan, Forster, & Frost, 1997). Two groups of Persian-speaking English language learners were tested on cognate and noncognate translation pairs in Persian-English and English-Persian directions with...
متن کامل$p$-adic Dual Shearlet Frames
We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...
متن کاملON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS
A t-Cayley hypergraph X = t-Cay(G; S) is called normal for a finite group G, if the right regular representationR(G) of G is normal in the full automorphism group Aut(X) of X. In this paper, we investigate the normality of t-Cayley hypergraphs of abelian groups, where S < 4.
متن کامل