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- Author: Sven Bodo Wirsing
- Publisher: Anchor Academic Publishing
- Year: 2018
- Pages: 260
- ISBN-10: 3960672217
- ISBN-13: 9783960672210
- Format: 14.8 x 21 x 1.4 cm, minkšti viršeliai
- Language: English
- SAVE -10% with code: EXTRA
Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises (e-book) (used book) | bookbook.eu
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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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- Author: Sven Bodo Wirsing
- Publisher: Anchor Academic Publishing
- Year: 2018
- Pages: 260
- ISBN-10: 3960672217
- ISBN-13: 9783960672210
- Format: 14.8 x 21 x 1.4 cm, minkšti viršeliai
- Language: English English
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.
Reviews