Related papers: Nested Artin approximation
This paper is a natural continuation of the study of skew power series rings A initiated in [P. Schneider and O. Venjakob, On the codimension of modules over skew power series rings with applications to Iwasawa algebras, J. Pure Appl.…
We define an Artin prime for an integer $g$ to be a prime such that $g$ is a primitive root modulo that prime. Let $g\in \mathbb{Z}\setminus\{-1\}$ and not be a perfect square. A conjecture of Artin states that the set of Artin primes for…
In this note we give a short and elementary proof for a part of Amitsur's noncrossed product theorem. Our approach does not rely on well-known results of valuation theory. Instead, we employ some preliminary properties of the unit groups of…
In this note we introduce central linear Armendariz rings as a generalization of Armendariz rings and investigate their properties.
An even Artin group is a group which has a presentation with relations of the form $(st)^n=(ts)^n$ with $n\ge 1$. With a group $G$ we associate a Lie $\mathbb Z$-algebra $\mathcal{TG}r(G)$. This is the usual Lie algebra defined from the…
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…
Derivative-matching approximations are constructed as power series built from functions. The method assumes the knowledge of special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented…
The parquet approximation in the matrix Higgs model is considered. We demonstrate analytically that in the large $N$ limit the parquet approximation gives an satisfying agreement with the exact results. It is shown that the parquet planar…
In this paper, we explore identities that allow for representation of positive integers raised to positive integral powers as sums of nested sums of smaller positive integral powers. We begin by establishing the base identity involving…
This short note delivers, via elementary calculations, a product representation of pi.
We prove a differential version of the Artin-Rees lemma with the use of Noetherian differential operators. As a consequence, we obtain several uniformity results for nonreduced rings.
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
We present a simpler proof of Naji's characterization of circle graphs.
By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate…
We revisit Christol's theorem on algebraic power series in positive characteristic and propose yet another proof for it. This new proof combines several ingredients and advantages of existing proofs, which make it very well-suited for…
Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representatons of the corresponding Artin group A. The poset…
In this paper, we sharpen a theorem of Artin to show that for a finite group, the dimension of the subspace of class functions spanned by the rational valued characters equals the number of conjugacy classes of cyclic subgroups.
We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.
Using notions of homogeneity we give new proofs of M. Artin's algebraicity criteria for functors and groupoids. Our methods give a more general result, unifying Artin's two theorems and clarifying their differences.