Bâtiment de l'Université d'Artois sous la neige

Séminaire d'algèbre et de géométrie du 07-11-2022

Exposé de Masood Aryapoor

Le 07-11-2022 à 15:00, en P108.

Algebraically closed σ-fields and δ-fields

Informations de connexion



Based on the notion of a skew root of a skew polynomial, we will investigate the concept of algebraically closed σ-fields and δ-fields. In contrast to the classical situation, it turns out that there are different notions of algebraic closedness. As an example of algebraic closedness, we will show that any commutative field K, equipped with an endomorphism σσ, can be embedded into a commutative field L such that every skew polynomial in L[T; σ] has a skew root. We will also explain that a similar result holds for (commutative) fields equipped with derivations. At the end of the talk, we will give an application regarding partial fraction decomposition in the skew field of rational skew functions.