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

Bag om 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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  • Sprog:
  • Engelsk
  • ISBN:
  • 9783960672210
  • Indbinding:
  • Paperback
  • Sideantal:
  • 260
  • Udgivet:
  • 3. december 2018
  • Størrelse:
  • 210x148x14 mm.
  • Vægt:
  • 313 g.
  • 8-11 hverdage.
  • 13. december 2024
Forlænget returret til d. 31. januar 2025

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Beskrivelse af 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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