A question on the discriminants of involutions of central division algebras

1993 ◽  
Vol 297 (1) ◽  
pp. 575-580 ◽  
Author(s):  
R. Parimala ◽  
R. Sridharan ◽  
V. Suresh
Keyword(s):  
Division Algebras ◽  
Central Division

scholarly journals EUCLIDEAN MINIMA AND CENTRAL DIVISION ALGEBRAS

2009 ◽  
Vol 05 (07) ◽  
pp. 1155-1168 ◽  
Author(s):  
EVA BAYER-FLUCKIGER ◽  
JEAN-PAUL CERRI ◽  
JÉRÔME CHAUBERT
Keyword(s):  
Number Field ◽  
Division Algebras ◽  
Central Division

The notion of Euclidean minimum of a number field is a classical one. In this paper, we generalize it to central division algebras and establish some general results in this new context.

scholarly journals Nicely semiramified division algebras over Henselian fields

2005 ◽  
Vol 2005 (4) ◽  
pp. 571-577 ◽  
Author(s):  
Karim Mounirh
Keyword(s):  
Division Algebra ◽  
Division Algebras ◽  
Central Division ◽  
Field Extensions ◽  
Finite Dimensional ◽  
Central Division Algebra ◽  
Radical Type ◽  
Maximal Subfield

This paper deals with the structure of nicely semiramified valued division algebras. We prove that any defectless finite-dimensional central division algebra over a Henselian fieldEwith an inertial maximal subfield and a totally ramified maximal subfield (not necessarily of radical type) (resp., split by inertial and totally ramified field extensions ofE) is nicely semiramified.

scholarly journals Correction to: “Realizing central division algebras”

1987 ◽  
Vol 130 (2) ◽  
pp. 397-399
Author(s):  
Richard Pierce ◽  
Charles Vinsonhaler
Keyword(s):  
Division Algebras ◽  
Central Division

scholarly journals Levels of division algebras

1990 ◽  
Vol 32 (3) ◽  
pp. 365-370 ◽  
Author(s):  
David B. Leep
Keyword(s):  
Function Field ◽  
Algebraic Extension ◽  
Global Field ◽  
Real Closed Field ◽  
Closed Field ◽  
Division Algebras ◽  
Central Division ◽  
Product Level ◽  
Euclidean Field ◽  
Finite Dimensional

In [7] the level, sublevel, and product level of finite dimensional central division algebras D over a field F were calculated when F is a local or global field. In Theorem 1.4 of this paper we calculate the same quantities if all finite extensions K of F satisfy ū(K) ≤2, where ū is the Hasse number of a field as defined in [2]. This occurs, for example, if F is an algebraic extension of the function field R(x) where R is a real closed field or hereditarily Euclidean field (see [4]).

scholarly journals Division algebras that generalize Dickson semifields

2020 ◽  
Vol 28 (2) ◽  
pp. 89-102
Author(s):  
Daniel Thompson
Keyword(s):  
Division Algebras ◽  
Central Simple Algebras ◽  
Central Division ◽  
Simple Algebras ◽  
Dimension 2 ◽  
Central Simple

AbstractWe generalize Knuth's construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension 2s2 by doubling central division algebras of degree s. Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

scholarly journals A note on Clifford algebras and central division algebras with involution

1985 ◽  
Vol 26 (2) ◽  
pp. 171-176 ◽  
Author(s):  
D. W. Lewis
Keyword(s):  
Quadratic Form ◽  
Clifford Algebra ◽  
Division Algebra ◽  
Clifford Algebras ◽  
Matrix Ring ◽  
Division Algebras ◽  
Central Division

In this note we consider the question as to which central division algebras occur as the Clifford algebra of a quadratic form over a field. Non-commutative ones other than quaternion division algebras can occur and it is also the case that there are certain central division algebras D which, while not themselves occurring as a Clifford algebra, are such that some matrix ring over D does occur as a Clifford algebra. We also consider the further question as to which involutions on the division algebra can occur as one of two natural involutions on the Clifford algebra.

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