Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises

Sven Bodo Wirsing

ISBN 10: 3960672217 / ISBN 13: 9783960672210

Edité par Anchor Academic Publishing, 2018

Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises | Sven Bodo Wirsing | Taschenbuch | 260 S. | Englisch | 2018 | Anchor Academic Publishing | EAN 9783960672210 | Verantwortliche Person für die EU: Bedey & Thoms Media GmbH, Björn Bedey, Hermannstal 119k, 22119 Hamburg, info[at]diplom[dot]de | Anbieter: preigu. N° de réf. du vendeur 115094237

Synopsis :

Within the context of the Wedderburn-Malcev theorem a radical complement exists and all complements are conjugated. The main topics of this work are to analyze the Determination of a (all) radical complements, the representation of an element as the sum of a nilpotent and fully separable element and the compatibility of the Wedderburn-Malcev theorem with derived structures. Answers are presented in details for commutative and solvable associative algebras. Within the analysis the set of fully-separable elements and the generalized Jordan decomposition are of special interest. We provide examples based on generalized quaternion algebras, group algebras and algebras of traingular matrices over a field. The results (and also the theorem of Wedderburn-Malcev and Taft) are transferred to non-unitary algebras by using the star-composition and the adjunction of an unit. Within the App endix we present proofs for the Wedderburn-Malcev theorem for unitary algebras, for Taft's theorem on G-invariant radical complements for unitary algebras and for a theorem of Bauer concerning solvable unit groups of associative algebras.

Détails bibliographiques

Titre : Separability within commutative and solvable...
Éditeur : Anchor Academic Publishing
Date d'édition : 2018
Reliure : Taschenbuch
Etat : Neu