Results 241 to 250 of about 1,407 (262)

Central simple algebras

2003
Skew fields are more complicated than fields and much less is known about them. However, in the case of division algebras (the case of finite dimension over the centre) the situation is rather better. It is convenient to include full matrix rings over division algebras, thus our topic in Section 5.1 is essentially the class of simple Artinian rings ...
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On extending Prüfer rings in central simple algebras

Forum Mathematicum, 2009
Many important properties of Prüfer domains extend to Prüfer orders \(S\) in a division algebra \(D\) [see \textit{J. H. Alajbegović} and \textit{N. I. Dubrovin}, J.~Algebra 135, No. 1, 165-176 (1990; Zbl 0718.16023)]. Recall that a Prüfer order \(S\) is characterized by the property that \(I^{-1}I=S\) and \(II^{-1}=O_l(I)\) holds for finitely ...
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CENTRAL SIMPLE -GRADED ALGEBRAS

Communications in Algebra, 2002
ABSTRACT In this paper we study central simple -graded K-algebras. We obtain structure theorems and define structure elements and invariants for these algebras and characterize their group of graded automorphisms. We define and study their genus and Brauer invariant. In the last part, we present a generalization of the Clifford algebras.
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Invariants for Equivalence of Central Simple G-algebras

Acta Applicandae Mathematicae, 2008
Clifford classes are equivalence classes of central simple \(G\)-algebras over fields, and they can be used to describe the Clifford theory of finite groups. The equivalence between two central simple \(G\)-algebras is defined in a way similar to the classical definition of the Brauer group, see for example [\textit{A. Turull}, J. Algebra 170, No.
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Generic Splitting Fields of Central Simple Algebras

The Annals of Mathematics, 1955
if and only if 5F splits W[. The extension of this result is the main object of the present paper. In contrast with the method of Witt, which uses the theory of the arithmetics of these function fields, the present method aims to obtain a generic condition forafield to split a given c.s.a. 2I. It is shown that to every c.s.a. ?
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A Double-Centralizer Theorem for Simple Associative Algebras

Canadian Journal of Mathematics, 1969
Consider the following result.PROPOSITION. Let D be a finite-dimensional central division algebra over a field F, and let Dn be the algebra (over F) of all n × n matrices with entries in D. Let A and B be in Dn, and suppose that BX = XB for every X in Dn such that XA = AX.
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Central simple algebras

2013
Grégory Berhuy, Frédérique Oggier
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Prescribed behavior of central simple algebras after scalar extension

Journal of Algebra, 2012
Sergey V Tikhonov
exaly  

A Decomposition Theorem for CK1of Central Simple Algebras

Communications in Algebra, 2006
Roozbeh Hazrat
exaly  

Cohomological invariants of central simple algebras of degree 4

Archiv Der Mathematik, 2012
Sanghoon Baek, Gregory Berhuy
exaly