Division Algebras over Henselian Fields
Bill Jacob,Adrian R. Wadsworth +1 more
172
TL;DR: In this paper, the authors focus on the tame division algebras D with center a field F with Henselian valuation v. As usual, they approach this by first obtaining results for graded division algebra, then lifting back from \(\operatorname {\mathsf {gr}}(D)\) to D. This is facilitated by results in §8.4.
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About: This article is published in Journal of Algebra. The article was published on 01 Jan 1990. and is currently open access. The article focuses on the topics: Center (category theory) & Division algebra.
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Citations
•Book
Graded Rings and Graded Grothendieck Groups
Roozbeh Hazrat
- 28 Jul 2016
TL;DR: The first systematic account of the graded Grothendieck group, a powerful invariant in algebra which has recently been adopted to classify the Leavitt path algebras, can be found in this paper.
Correspondences Between Valued Division Algebras and Graded Division Algebras
TL;DR: In this article, it was shown that the map [D]↦[GD]g yields an index-preserving isomorphism from the tame part of the Brauer group of F to the graded Brauer groups of GF.
58
Finite-Dimensional Division Algebras
V. P. Platonov,V. I. Yanchevskii +1 more
- 01 Jan 1996
TL;DR: In this article it was shown that Frobenius proved that over the field of real numbers there exists no non-commutative division algebra apart from Hamilton's quaternions.
42
Le gradué d’une algèbre à division valuée
TL;DR: In this article, the gradue d'une algebre a division valuee is defined as the gradient of a division with respect to the division value value of the division.
28
References
•Book
Structure of Algebras
A. Adrian Albert
- 01 Jan 1939
TL;DR: The structure theorems of Wedderburn Simple algebras Crossed products and exponents Cyclic semi-fields Cyclic algeses and $p$ algebases Representations and Riemann matrices Rational division algesbras Involutions of algesbases Special results as discussed by the authors
The Brauer group of a commutative ring
Maurice Auslander,Oscar Goldman +1 more
TL;DR: In this article, it was shown that a considerable portion of the classical theory of separability is preserved in the generalization of separable algebras over arbitrary commutative rings.
•Journal Article
Algèbres à division et extensions de corps sauvagement ramifiées de degré premier
TL;DR: La theorie des valuations sur les algebres ä division (ou corps non commutatifs) a connu ces dernieres annees un developpement considerable, justifie par ses applications ä la construction de certains (contre-) exemples donnant la solution de plusieurs problemes classiques as discussed by the authors.
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