Book Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-Unitar Sven Bodo Wirsing

portada Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-Unitary Algebras. With 401 Exercises

Type

Physical Book

Publisher

Anchor Academic Publishing

Author

Sven Bodo Wirsing

Year

2018

Language

English

Pages

260

Format

Paperback

ISBN13

9783960672210

Synopsis "Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-Unitary Algebras. With 401 Exercises"

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.

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Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-Unitary Algebras. With 401 Exercises - Sven Bodo Wirsing

Synopsis "Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-Unitary Algebras. With 401 Exercises"

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