Related papers: Nested Artin approximation

We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…

Some projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T were constructed in [3]. In this paper we describe their integer cohomology rings by generators and relations.

For a given finitely generated multiplicative subgroup of the rationals which possibly contain negative numbers, we derive, subject to GRH, formulas for the densities of primes for which the index of the reduction group has a given value.…

Nested words, a model for recursive programs proposed by Alur and Madhusudan, have recently gained much interest. In this paper we introduce quantitative extensions and study nested word series which assign to nested words elements of a…

This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.

A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.

This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of…

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and…

In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.

We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…

We show that the pair given by the power set and by the "Grassmannian"(set of all subgroups) of an arbitrary group behaves very much like the pair given by a projective space and its dual projective space. More precisely, we generalize…

Consider (analytic, resp. algebraic) map-germs, Maps((k^n,o),(k^m,o)). These germs are traditionally studied up to the right, let-right and contact equivalences. Below G is one of these groups. An important tool in this study is the Artin…

We prove the following CR version of Artin's approximation theorem for holomorphic mappings between real-algebraic sets in complex space. Let $M\subset \C^N$ be a real-algebraic CR submanifold whose CR orbits are all of the same dimension.…

The representation dimension of an artin algebra as introduced by M.Auslander in his Queen Mary Notes is the minimal possible global dimension of the endomorphism ring of a generator-cogenerator. The paper is based on two texts written in…

In arXiv:0910.1727 we find certain finite homomorphic images of Artin braid group into appropriate symmetric groups, which a posteriori are extensions of the symmetric group on n letters by an abelian group. The main theorem of this paper…

The aim of this note is to give a simpler proof of a result of Avsec, which states that $q$-Gaussian algebras have the complete metric approximation property.

Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.

The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In…

We establish the tracial stability of a certain class of graph products of C*-algebras. This result involves the development of the "pincushion class" of finite graphs. We then apply this result in two ways. The first application yields a…

This work concerns the study of properties of a group of Koszul algebras coming from the toric ideals of a chordal bipartite infinite family of graphs (alternately, these rings may be interpreted as coming from determinants of certain…