Results 211 to 220 of about 8,728,657 (238)
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Israel Journal of Mathematics, 1978
Wedderburn’s factorization of polynomials over division rings is refined and used to prove that every central division algebra of degree 8, with involution, has a maximal subfield which is a Galois extension of the center (with Galois group Z2⊕Z2⊕Z2). The same proof, for an arbitrary central division algebra of degree 4, gives an explicit construction ...
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Wedderburn’s factorization of polynomials over division rings is refined and used to prove that every central division algebra of degree 8, with involution, has a maximal subfield which is a Galois extension of the center (with Galois group Z2⊕Z2⊕Z2). The same proof, for an arbitrary central division algebra of degree 4, gives an explicit construction ...
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1994
The Wedderburn-Artin theorem reduces the study of semisimple algebras to the description of division algebras over a field K. If D is a finite dimensional division algebra over K and C its center, then C is a field (an extension of the field K) and D can be considered as an algebra over the field C.
Yurij A. Drozd, Vladimir V. Kirichenko
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The Wedderburn-Artin theorem reduces the study of semisimple algebras to the description of division algebras over a field K. If D is a finite dimensional division algebra over K and C its center, then C is a field (an extension of the field K) and D can be considered as an algebra over the field C.
Yurij A. Drozd, Vladimir V. Kirichenko
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1993
In the first two chapters we studied rings and modules. Many of the important examples we studied, such as polynomial rings, matrix rings, group rings and the quaternions, have additional structure we have been ignoring; namely, they are modules as well as rings, and the ring multiplication is compatible with the module multiplication.
Benson Farb, R. Keith Dennis
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In the first two chapters we studied rings and modules. Many of the important examples we studied, such as polynomial rings, matrix rings, group rings and the quaternions, have additional structure we have been ignoring; namely, they are modules as well as rings, and the ring multiplication is compatible with the module multiplication.
Benson Farb, R. Keith Dennis
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Central Simple Algebras and Galois Cohomology
2006The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by ...
Philippe Gille, Tamás Szamuely
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Some Results on Central Simple Algebras
The Annals of Mathematics, 1956The present note is a continuation of the first part of [2].' The results of that part are applied here to obtain some new results on central simple algebras and some old ones in a new way. The first application is to the representation theory of the full linear group GL(n).
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Construction of Central Simple Associative Algebras
The Annals of Mathematics, 1944The theory of crossed products is generalized to the case of a maximal subfield \(P\) of a central simple algebra \(\mathfrak A\) which is not necessarily galoisian over the ground field \(\Phi\). \(\mathfrak A\) is a double-module over \(P\) and defines a regular self-representation \(E\) of \(P\) [the author, Am. J. Math.
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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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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, 2009Many 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, 2002ABSTRACT 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, 2008Clifford 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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