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

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


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About the Book

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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Product Details
  • ISBN-13: 9783960672210
  • Publisher: Anchor Academic Publishing
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 363 gr
  • ISBN-10: 3960672217
  • Publisher Date: 03 Dec 2018
  • Height: 210 mm
  • No of Pages: 260
  • Spine Width: 14 mm
  • Width: 148 mm


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

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