These algebras determine, by the Sliedderburn Theorem. the semi-simple finite dimensional
algebras over a field. They lead to the definition of the Brauer group and to certain geometric …

If F is a field with a Henselian valuation v and D is a finite-dimensional division algebra over
F, it is known that u can be extended uniquely to a valuation on D. Thus, D has a valuation …

The theory of finite-dimensional division algebras witnessed several breakthroughs in the
latter decades of the twentieth century. Important advances, such as Amitsur's construction of …

The main result of this paper is the following: if (F, v) is a valued field, F h its Henselization, D
a division algebra with center F, and [D: F]<∞, then v extends to D iff D⊗ FF h is a division …

Let $ D $ and $ E $ be central division algebras over $ k $; let $ K $ be the generic splitting
field of $ E $; we show that the index of $ D {\otimes _k} K $ is the minimum of the indices of …

Valuation theory has classically meant the study of valuations on a commutative eld. Such
valuation theory has ourished for many decades, nourished by its connections with number …

Open problems on central simple algebras | SpringerLink Skip to main content Advertisement
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Transformation …

We provide a detailed study of torsors over Laurent polynomial rings under the action of an
algebraic group. As applications we obtained variations of Raghunathan's results on torsors …

If D is a tame central division algebra over a Henselian valued field F, then the valuation on
D yields an associated graded ring GD which is a graded division ring and is also central …

We introduce a type of value function $ y $ called a gauge on a finite-dimensional
semisimple algebra $ A $ over a field $ F $ with valuation $ v $. The filtration on $ A …