ANNIHILATORS IN IDEALS OF COEFFICIENTS OF ZERO-DIVIDING POLYNOMIALS

Annihilators of Ideals of Exterior Algebras

The Orlik-Solomon algebra A of a matroid is isomorphic to the quotient of an exterior algebra E by a defining ideal I . We find an explicit presentation of the annihilator ideal of I or, equivalently, the E-module dual to A. As an application of that we provide a necessary, combinatorial condition for the algebra A to be quadratic. We show that this is stronger than matroid being line-closed th...

Irreducible polynomials with consecutive zero coefficients

Given an integer n > 1, it has been proved independently by S.D. Cohen [2] and R. Ree [13], that for all large enough q, there always is an irreducible polynomial over Fq of the form T +T +a. However, much less is known when q is fixed and n large. In [10], T. Hansen and G.L. Mullen conjecture that given integers n > m ≥ 0 there exists a monic irreducible polynomial over Fq of degree n with the...

Annihilators of Local Cohomology in Characteristic Zero

This paper discusses the problem of whether it is possible to annihilate elements of local cohomology modules by elements of arbitrarily small order under a fixed valuation. We first discuss the general problem and its relationship to the Direct Summand Conjecture, and next present two concrete examples where annihilators with small order are shown to exist. We then prove a more general theorem...

Integral closure of ideals and annihilators of homology

Coefficients of cyclotomic polynomials

Let a(n, k) be the k-th coefficient of the n-th cyclotomic polynomial. Recently, Ji, Li and Moree [12] proved that for any integer m ≥ 1, {a(mn, k)|n, k ∈ N} = Z. In this paper, we improve this result and prove that for any integers s > t ≥ 0, {a(ns + t, k)|n, k ∈ N} = Z. 2000 Mathematics Subject Classification:11B83; 11C08