Central division algebras - Open Access .click

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ON THE CLASSIFICATION OF CENTRALLY FINITE ALTERNATIVE DIVISION RINGS SATISFYING ALGEBRAIC CLOSURE CONDITIONS

Journal of Algebra and Its Applications, 2012
In this paper, we prove that the rings of quaternions and of octonions over an arbitrary real closed field are algebraically closed in the sense of Eilenberg and Niven. As a consequence, we infer that some reasonable algebraic closure conditions, including the one of Eilenberg and Niven, are equivalent on the class of centrally finite alternative ...
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A Reduced-Trace-Zero Element That Is Not a Commutator in a Central Division Algebra

15 ...
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Locally finite-dimensional central division algebras over function fields of curves over m-local fields, criterion for normality

Let $K _{m}$ be an $m$-local field with an $m$-th residue field $K _{0}$, for some integer $m > 0$, and let $K/K _{m}$ be a field extension of transcendence degree $1$. The paper under review shows that if $K _{0}$ is a field of finite Diophantine dimension ddim$(K _{0})$, and $R$ is an associative locally finite-dimensional central division $K ...
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A Decomposition Theorem for CK1of Central Simple Algebras

Communications in Algebra, 2006
Roozbeh Hazrat
exaly

Hyperbolic Weyl groups and the four normed division algebras

Journal of Algebra, 2009
Alex Feingold, Hermann Nicolai
exaly

Selectivity in division algebras

Archiv Der Mathematik, 2014
Luis Arenas-Carmona
exaly

Division Algebras with Left Algebraic Commutators

Algebras and Representation Theory, 2017
Saieed Akbari, Mehdi Aaghabali, Mai Hoang Bien +2 more
exaly

Symbol p-algebras of prime degree and their p-central subspaces

Archiv Der Mathematik, 2016
Adam Chapman
exaly

Common subfields of $p$-algebras of prime degree

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2015
Adam Chapman
exaly