Related papers: Annihilating polynomials for quadratic forms and S…

We establish effective equidistribution theorems, with a polynomial error rate, for orbits of unipotent subgroups in quotients of quasi-split, almost simple Linear algebraic groups of absolute rank 2. As an application, inspired by the…

We show that any nonzero polynomial in the ideal generated by the $r \times r$ minors of an $n \times n$ matrix $X$ can be used to efficiently approximate the determinant. For any nonzero polynomial $f$ in this ideal, we construct a small…

For a commutative ring R we investigate the property that the sets of minimal primes of finitely generated ideals of R is always finite. We prove this property passes to polynomial ring extensions (in an arbitrary number of variables) over…

We demonstrate that the Schr\"odinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational…

In this paper, we consider the degenerate Stirling polynomials of the second kind which are derived from the generating function. In addition, we give some new identities for these polynomials.

To each Galois extension $L/K$ of number fields with Galois group $G$ and each integer $r \leq 0$ one can associate Stickelberger elements in the centre of the rational group ring $\mathbb{Q}[G]$ in terms of values of Artin $L$-series at…

In this work, we present a generalization to varieties and sheaves of the fundamental ideal of the Witt ring of a field by defining a sheaf of fundamental ideals $\tilde{I}$ and a sheaf of Witt rings $\tilde{W}$ in the obvious way. The…

Relying on the classical second moment formula of Rogers we give an effective asymptotic formula for the number of integer vectors $v$ in a ball of radius $t$, with value $Q(v)$ in a shrinking interval of size $t^{-\kappa}$, that is valid…

We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…

The paper addresses a conjecture of Shapiro and Tater on the similarity between two sets of points in the complex plane; on one side is the values of $t\in \mathbb{C}$ for which the spectrum of the quartic anharmonic oscillator in the…

A rational positive-definite quadratic form is perfect if it can be reconstructed from the knowledge of its minimal nonzero value m and the finite set of integral vectors v such that f(v) = m. This concept was introduced by Voronoi and…

We provide a sufficient condition for a polynomial ring, not necessarily commutative, to have a first-order definition for the rational integers.

Let $R=k[x,y,z]$ be a standard graded $3$-variable polynomial ring, where $k$ denotes any field. We study grade $3$ homogeneous ideals $I \subseteq R$ defining compressed rings with socle $k(-s)^{\ell} \oplus k(-2s+1)$, where $s \geq3$ and…

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over a field $K$, and let $A$ be a finitely generated standard graded $S$-algebra. We show that if the defining ideal of $A$ has a quadratic initial ideal, then all the graded components of…

This paper is concerned with weak* closed masa-bimodules generated by A(G)-invariant subspaces of VN(G). An annihilator formula is established, which is used to characterise the weak* closed subspaces of B(L^2(G)) which are invariant under…

We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the…

We study the annihilator of the cokernel of a map of free Z/2-graded modules over a Z/2-graded skew-commutative algebra in characteristic 0 and define analogues of its Fitting ideals. We show that in the ``generic'' case the annihilator is…

Let $S=\mathbb{K}[x_1,\ldots,x_n]$ the polynomial ring over a field $\mathbb{K}$. In this paper for some families of monomial ideals $I \subset S$ we study the minimal number of generators of $I^k$. We use this results to find some other…

The purpose of this paper is to prove that the symbolic Rees rings of ideals defining certain finite sets of points in the projective plane over an algebraically closed field are finitely generated using a ring theoretical criterion which…

In this paper we continue our study of annihilating-ideal graph of commutative rings, that was introduced in Part I (see [5]). Let $R$ be a commutative ring with ${\Bbb{A}}(R)$ its set of ideals with nonzero annihilator and $Z(R)$ its set…