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

Wirsing, Sven Bodo

Couverture souple

ISBN 10 : 3960672217 ISBN 13 : 9783960672210

Editeur : Anchor Academic Publishing, 2018

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 de l'édition

• Éditeur: Anchor Academic Publishing
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 3960672217
• ISBN 13: 9783960672210
• Reliure: Broché
• Nombre de pages: 260
• Coordonnées du fabricant: Bedey & Thoms Media GmbH; info@diplom.de; ; Hermannstal 119 k; Hamburg; 22119; Allemagne