arXiv math/07030382007-03math.RA

A twisted Laurent series ring that is a noncrossed product

Timo Hanke

备注：: 4 pages (A4), updated version of published paper, the sign error in the definition of the element πhas been corrected
发表信息：: Israel J. Math., vol. 150 (2005), p. 199--204

英文摘要：

The striking results on noncrossed products were their existence (Amitsur) and the determination of Q(t) and Q((t)) as their smallest possible centres (Brussel). This paper gives the first fully explicit noncrossed product example over Q((t)). As a consequence, the use of deep number theoretic theorems (local-global principles such as the Hasse norm theorem and density theorems) in order to prove existence is eliminated. Instead, the example can be verified by direct calculations. The noncrossed product proof is short and elementary.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

关于 Amitsur 非交叉积定理的一个注记

A note on Amitsur's noncrossed product theorem

本文为 Amitsur 非交叉积定理的部分内容提供了一种简短初等的证明，该方法不依赖赋值论，而是利用形式迭代 Laurent 级数除环单位群的性质。

2024-01-07math.RA

Noncrossed products in Witt's Theorem

Since Amitsur's discovery of noncrossed product division algebras more than 35 years ago, their existence over more familiar fields has been an object of investigation. Brussel's work was a culmination of this effort, exhibiting noncrossed products over the rational function field k(t) and the Laurent series field k((t)) over any global field k -- the smallest possible centers of noncrossed products. Witt's theorem gives a transparent description of the Brauer group of k((t)) as the direct sum of the Brauer group of k and the character group of the absolute Galois group of k. We classify the B…

2009-05-21math.NTmath.RA

A Direct Approach to Noncrossed Product Division Algebras

A valuation theoretic approach is presented that directly leads to division algebras that are noncrossed products (instead of, e.g., describing Brauer classes of noncrossed products in an abstract manner). While this feature is shared by Amitsur's original construction, the new approach works over small fields. It is further demonstrated how it can be used to obtain very explicit examples of noncrossed products in the form of iterated twisted function fields over division algebras over global fields. The examples allow even to write down structure constants of noncrossed products.

2011-09-07math.NTmath.RA

On absolute Galois splitting fields of central simple algebras

A splitting field of a central simple algebra is said to be absolute Galois if it is Galois over some fixed subfield of the centre of the algebra. The paper provides an existence theorem for such fields over global fields with enough roots of unity. As an application, all twisted function fields and all twisted Laurent series rings over symbol algebras (or p-algebras) over global fields are crossed products. A closely related statement holds for division algebras over Henselian valued fields with global residue field. The existence of absolute Galois splitting fields in central simple algebras…

2007-02-23math.NTmath.RA

Goldie twisted partial skew power series rings

In this article, we work with unital twisted partial action of $\mathbb{Z}$ on an unital ring $R$ and we introduce the twisted partial skew power series rings and twisted partial skew Laurent series rings. We study primality, semi-primality and prime ideals in these rings. We completely describe the prime radical in partial skew Laurent series rings. Moreover, we study the Goldie property in partial skew power series rings and partial skew Laurent series rings and we describe conditions of the semiprimality of twisted partial skew power series rings.

2017-09-28math.RA

Quasi-Lie structure of twisted derivations of Laurent polynomials

Hartwig, Larsson and the second author in [J. Algebra, 2005] defined a bracket on sigma-derivations of a commutative algebra. We show that this bracket preserves inner derivations, and based on this obtain some structural results on sigma-derivations on Laurent polynomials in one variable.

2006-08-18math.QAmath.RA

更多相关论文收起更多论文

Isotopes of Octonion Algebras, G2-Torsors and Triality

Octonion algebras over rings are, in contrast to those over fields, not determined by their norm forms. Octonion algebras whose norm is isometric to the norm q of a given algebra C are twisted forms of C by means of the Aut(C)-torsor O(q) ->O(q)/Aut(C). We show that, over any commutative unital ring, these twisted forms are precisely the isotopes C(a,b) of C, with multiplication given by x*y=(xa)(by), for unit norm octonions a,b of C. The link is provided by the triality phenomenon, which we study from new and classical perspectives. We then study these twisted forms using the interplay, thus …

2017-11-21math.RA

The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings

Given a projective scheme $X$ over a field $k$, an automorphism $σ$ of $X$, and a $σ$-ample invertible sheaf $L$, one may form the twisted homogeneous coordinate ring $B = B(X, L, σ)$, one of the most fundamental constructions in noncommutative projective algebraic geometry. We study the primitive spectrum of $B$, as well as that of other closely related algebras such as skew and skew-Laurent extensions of commutative algebras. Over an algebraically closed, uncountable field $k$ of characteristic zero, we prove that that the primitive ideals of $B$ are characterized by the usual Dixmier-Moegli…

2008-12-17math.AGmath.RA

具有 McCoy 性质的斜广义幂级数环

Skew Generalized Power Series Rings With the McCoy Property

本文研究了斜广义幂级数环上的 $(S,ω)$-McCoy 条件，将标准 McCoy 条件从多项式推广至斜广义幂级数，并推广了相关现有结果。

2025-04-27math.RAmath.RT

代数 $K$-理论中强 $\mathbb{Z}$-分级环的‘基本定理’

The "fundamental theorem" for the algebraic $K$-theory of strongly $\mathbb{Z}$-graded rings

Queen's University Belfast（贝尔法斯特女王大学）

本文研究了强 $\mathbb{Z}$-分级环的代数 $K$-理论，证明了在经典情况下，Laurent多项式环的 $K$-群可以表示为原环 $L$ 的 $K$-群的直接和，以及某些‘nil’群；并进一步推广了这一结果，涉及与分级结构相关的 $L$-模的移位作用，以及将‘nil’群识别为同调 nilpotent 旋转变换的减少 $K$-理论，并建立了类似 Mayer-Vietoris 和局部化序列的类比。

2020-03-31math.KTmath.RA