Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-unitary Algebras. With 401 Exercises
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| Title: | Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-unitary Algebras. With 401 Exercises |
|---|---|
| Description: | 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 triangular 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 Appendix 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. |
| Authors: | Wirsing, Sven Bodo |
| Resource Type: | eBook. |
| Subjects: | Separable algebras, Commutative algebra, Associative algebras |
| Categories: | MATHEMATICS / Algebra / Intermediate |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Header | DbId: nlebk DbLabel: eBook Collection (EBSCOhost) An: 2070397 RelevancyScore: 1084 AccessLevel: 6 PubType: eBook PubTypeId: ebook PreciseRelevancyScore: 1083.55249023438 |
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| Items | – Name: Title Label: Title Group: Ti Data: Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-unitary Algebras. With 401 Exercises – Name: Abstract Label: Description Group: Ab Data: 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 triangular 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 Appendix 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. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wirsing%2C+Sven+Bodo%22">Wirsing, Sven Bodo</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Separable+algebras%22">Separable algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Commutative+algebra%22">Commutative algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Associative+algebras%22">Associative algebras</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Algebra+%2F+Intermediate%22">MATHEMATICS / Algebra / Intermediate</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 512.4 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Separable algebras Type: general – SubjectFull: Commutative algebra Type: general – SubjectFull: Associative algebras Type: general Titles: – TitleFull: Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-unitary Algebras. With 401 Exercises Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wirsing, Sven Bodo – PersonEntity: Name: NameFull: Wirsing, Sven Bodo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2018 – D: 30 M: 03 Type: profile Y: 2019 Identifiers: – Type: isbn-print Value: 9783960672210 – Type: isbn-electronic Value: 9783960677215 Titles: – TitleFull: Separability Within Commutative and Solvable Associative Algebras. Under Consideration of Non-unitary Algebras. With 401 Exercises Type: main |
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