• Corpus ID: 16335479

Localisations and Completions of Skew Power Series Rings

  title={Localisations and Completions of Skew Power Series Rings},
  author={Peter Schneider and Otmar Venjakob},
  journal={arXiv: Rings and Algebras},
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. Algebra 204 (2005), 349 - 367.]. We construct skew Laurent series rings B and show the existence of some canonical Ore sets S for the skew power series rings A such that a certain completion of the localisation A_S is isomorphic to B. This is applied to certain… 

Skew power series rings over a prime base ring

In this paper, we investigate the structure of skew power series rings of the form S = R [[ x ; σ, δ ]], where R is a complete, positively filtered ring and ( σ, δ ) is a skew derivation respecting

Dimension Theory in Iterated Local Skew Power Series Rings

  • Billy Woods
  • Mathematics
    Algebras and Representation Theory
  • 2022
Many well-known local rings, including soluble Iwasawa algebras and certain completed quantum algebras, arise naturally as iterated skew power series rings. We calculate their Krull and global

Goldie Ranks of Skew Power Series Rings of Automorphic Type

Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B: = A[[y; α]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We

On prime ideals of noetherian skew power series rings

We study prime ideals in skew power series rings T:= R[[y; τ, δ]], for suitably conditioned complete right Noetherian rings R, automorphisms τ of R, and τ-derivations δ of R. Such rings were

On prime ideals of noetherian skew power series rings

We study prime ideals in skew power series rings T:= R[[y; τ, δ]], for suitably conditioned complete right Noetherian rings R, automorphisms τ of R, and τ-derivations δ of R. Such rings were

Exactness of the reduction on étale modules

On a Localisation Sequence for the K-Theory of Skew Power Series Rings

Let $B=A[[t;\sigma,\delta]]$ be a skew power series ring such that $\sigma$ is given by an inner automorphism of $B$. We show that a certain Waldhausen localisation sequence involving the K-theory of

The Algebra of Formal Twisted Pseudodifferential Symbols and a Noncommutative Residue

Motivated by Connes–Moscovici’s notion of a twisted spectral triple, we define an algebra of formal twisted pseudodifferential symbols with respect to a twisting of the base algebra. We extend the

(\phi,\Gamma)-modules over noncommutative overconvergent and Robba rings

We construct noncommutative multidimensional versions of overconvergent power series rings and Robba rings. We show that the category of \'etale $(\varphi,\Gamma)$-modules over certain completions of

The main conjecture of Iwasawa theory for totally real fields

Let p be an odd prime. Let $\mathcal{G}$ be a compact p-adic Lie group with a quotient isomorphic to ℤp. We give an explicit description of K1 of the Iwasawa algebra of $\mathcal{G}$ in terms of

Primeness, semiprimeness and localisation in Iwasawa algebras

Necessary and sufficient conditions are given for the completed group algebras of a compact p-adic analytic group with coefficient ring the p-adic integers or the field of p elements to be prime,

A noncommutative Weierstrass preparation theorem and applications to Iwasawa theory

In this paper and a forthcoming joint one with Y. Hachimori we study Iwasawa modules over an infinite Galois extension K of a number field k whose Galois group G=G(K/k) is isomorphic to the

The GL2 Main Conjecture for Elliptic Curves without Complex Multiplication

Let G be a compact p-adic Lie group, with no element of order p, and having a closed normal subgroup H such that G/H is isomorphic to Zp. We prove the existence of a canonical Ore set S* of non-zero

Blowing up non-commutative smooth surfaces

In this paper we will think of certain abelian categories with favorable properties as non-commutative surfaces. We show that under certain conditions a point on a non-commutative surface can be

Graded Modules of Gelfand–Kirillov Dimension One over Three-Dimensional Artin–Schelter Regular Algebras

Abstract Let A be a three dimensional Artin–Schelter regular algebra. We give a description of the category of finitely generated A -modules of Gelfand–Kirillov dimension one (modulo those of finite

The Structure of Rings

In the first part of this chapter a general structure theory for rings is presented. Although the concepts and techniques introduced have widespread application, complete structure theorems are

Profinite Groups

γ = c0 + c1p + c2p + · · · = (. . . c3c2c1c0)p, with ci ∈ Z, 0 ≤ ci ≤ p− 1, called the digits of γ. This ring has a topology given by a restriction of the product topology—we will see this below. The


  • K. Ardakov
  • Mathematics
    Glasgow Mathematical Journal
  • 2006
Let $G$ be a compact $p$-adic analytic group and let $\Lambda_G$ be its completed group algebra with coefficient ring the $p$-adic integers $\mathbb{Z}_p$. We show that the augmentation ideal in

Noncommutative Noetherian Rings

Articles on the history of mathematics can be written from many dierent perspectives. Some aim to survey a more or less wide landscape, and require the observer to watch from afar as theories develop