Related papers: Simple-root bases for Shi arrangements
In this paper we partially settle our conjecture from [1] (math.SP/0701143) on roots of eigenpolynomials for degenerate exactly-solvable operators. Namely, for any such operator, we establish a lower bound (which supports our conjecture)…
We study the system of root functions (SRF) of Hill operator $Ly = -y^{\prime \prime} +vy $ with a singular potential $v \in H^{-1}_{per}$ and SRF of 1D Dirac operator $ Ly = i {pmatrix} 1 & 0 0 & -1 {pmatrix} \frac{dy}{dx} + vy $ with…
We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and…
We study a question which can be roughly stated as follows: Given a (unital or nonunital) algebra $A$ together with a Gr\"obner-Shirshov basis $G$, consider the free operated algebra $B$ over $A$, such that the operator satisfies some…
It is proved that every commutative ring whose RD-injective modules are $\Sigma$-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian…
We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…
In this paper, we compute the Gr\"obner-Shirshov bases for certain regular double extension algebras by means of an algorithm implemented in Matlab, which facilitates the underlying algebraic computations. Moreover, we establish that these…
In this paper, we present a new basis of polynomial over finite fields of characteristic two and then apply it to the encoding/decoding of Reed-Solomon erasure codes. The proposed polynomial basis allows that $h$-point polynomial evaluation…
Let $R$ be a ring with unity, $\sigma$ an endomorphism of $R$ and $M_R$ a right $R$-module. In this paper, we continue studding $\sigma$-rigid modules that were introduced by Gunner et al. \cite{generalized/rigid}. We give some results on…
Exceptional modules are tree modules. A tree module usually has many tree bases and the corresponding coefficient quivers may look quite differently. The aim of this note is to introduce a class of exceptional modules which have a…
We study the Schur elements associated to the simple modules of the Ariki-Koike algebra. We first give a cancellation-free formula for them so that their factors can be easily read and programmed. We then study direct applications of this…
In this paper, we make a conjecture (conjecture 1) related to the Bateman-Horn conjecture and proceed to study the roots of $x^2+1$ and $x^2+2$ to prime moduli, assuming the truth of the Bateman-Horn conjecture and conjecture 1 and using…
We verify a finiteness conjecture of Feit on sources of simple modules over group algebras for various classes of finite groups related to the symmetric groups.
The converse of Schur's lemma (or CSL) condition on a module category has been the subject of considerable study in recent years. In this note we extend that work by developing basic properties of module categories in which the CSL…
In this paper, we construct a canonical linear basis for free commutative integro-differential algebras by applying the method of Gr\"obner-Shirshov bases. We establish the Composition-Diamond Lemma for free commutative differential…
Developed by Buchberger for commutative polynomial rings, Groebner Bases are frequently applied to solve algorithmic problems, such as the congruence problem for ideals. Until now, these ideas have been transmitted to different in part…
For a homogeneous polynomial of $n$ variables, we present a new method to compute the roots of Bernstein-Sato polynomial supported at the origin, assuming that general hyperplane sections of the associated projective hypersurface have at…
The main result of this paper is a recursive description of all decompositions \[ \Delta^+ = \Phi_1 \sqcup \Phi_2 \sqcup \dots \sqcup \Phi_k \] of the positive roots $\Delta^+$ of an arbitrary root system $\Delta$ into a disjoint union of…
Our main result is to show that the existence of a root in. --$\alpha$--Nfor the p-th Bernstein polynomial of the (a,b)-module generated by a holomorphicform in the (convergent) Brieskorn (a,b)-module associated to f, under the hypothesis…
The Mitsch order is already known as a natural partial order for semigroups and rings. The purpose of this paper is to further study of the Mitsch order on modules by investigating basic properties via endomorphism rings. And so this study…