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![Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises](https://images.bod.com/images/separability-within-commutative-and-solvable-associative-algebras-under-consideration-of-non-unitary-algebras-with-401-exercises-sven-bodo-wirsing-9783960672210.jpg/500/500/Separability_within_commutative_and_solvable_associative_algebras._Under_consideration_of_non-unitary_algebras._With_401_exercises.webp)
Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises
Paperback
260 Seiten
ISBN-13: 9783960672210
Verlag: Anchor Academic Publishing
Erscheinungsdatum: 03.12.2018
Sprache: Englisch
49,99 €
inkl. MwSt. / portofrei
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Mehr InfosWithin 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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