Algebraic elements in division algebras over function fields of curves

1985 ◽  
Vol 52 (1-2) ◽  
pp. 33-45 ◽  
Author(s):  
Michel van den Bergh ◽  
Jan van Geel
Keyword(s):  
Function Fields ◽  
Division Algebras ◽  
Algebraic Elements

scholarly journals Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

2011 ◽  
Vol 226 (5) ◽  
pp. 4316-4337 ◽  
Author(s):  
E. Brussel ◽  
K. McKinnie ◽  
E. Tengan
Keyword(s):  
Function Fields ◽  
Division Algebras

Algebraic elements in matrix ring over division algebras

1995 ◽  
Vol 118 (2) ◽  
pp. 215-221
Author(s):  
A. I. Lichtman
Keyword(s):  
Finite Group ◽  
Matrix Ring ◽  
Quotient Ring ◽  
Arbitrary Field ◽  
Division Algebras ◽  
Nilpotent Radical ◽  
Ring Of Fractions ◽  
The Matrix ◽  
Algebraic Elements ◽  
Linear Envelope

Let K be an arbitrary field, G a polycyclic-by-finite group and A a prime ideal of the group ring KG. It is well known that the quotient ring (KG)/A is a Goldie ring; we denote by R its ring of fractions. Let U be a subgroup of units of the matrix ring Rn×n let K[U] be the linear envelope of U and let rad (K[U]) be the nilpotent radical of K [U].

On Asano’s theorem

2019 ◽  
Vol 18 (10) ◽  
pp. 1950181
Author(s):  
Münevver Pınar Eroǧlu ◽  
Tsiu-Kwen Lee ◽  
Jheng-Huei Lin
Keyword(s):  
Vector Space ◽  
Division Algebra ◽  
Division Algebras ◽  
Infinite Field ◽  
Additive Subgroup ◽  
Normal Bases ◽  
Algebraic Elements ◽  
Inner Automorphisms

Let [Formula: see text] be a division algebra over an infinite field [Formula: see text] such that every element of [Formula: see text] is a sum of finitely many algebraic elements. As a generalization of Asano’s theorem, it is proved that every noncentral subspace of [Formula: see text] invariant under all inner automorphisms induced by algebraic elements contains [Formula: see text], the additive subgroup of [Formula: see text] generated by all additive commutators of [Formula: see text]. From the viewpoint we study the existence of normal bases of certain subspaces of division algebras. It is proved among other things that [Formula: see text] is generated by multiplicative commutators as a vector space over the center of [Formula: see text].

scholarly journals Division algebras and maximal orders for given invariants

2016 ◽  
Vol 19 (A) ◽  
pp. 178-195 ◽  
Author(s):  
Gebhard Böckle ◽  
Damián Gvirtz
Keyword(s):  
Function Fields ◽  
Maximal Order ◽  
Global Field ◽  
Division Algebras ◽  
Wild Ramification ◽  
Maximal Orders ◽  
Cyclic Algebras

Brauer classes of a global field can be represented by cyclic algebras. Effective constructions of such algebras and a maximal order therein are given for$\mathbb{F}_{q}(t)$, excluding cases of wild ramification. As part of the construction, we also obtain a new description of subfields of cyclotomic function fields.

Division algebras over rational function fields in one variable

2005 ◽  
pp. 158-180 ◽  
Author(s):  
L. H. Rowen ◽  
A. S. Sivatski ◽  
J.-P. Tignol
Keyword(s):  
Rational Function ◽  
Function Fields ◽  
Division Algebras
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