Quadratic Division Algebras

DOI10.2307/1993623zbMath0136.30303OpenAlexW4230849898MaRDI QIDQ5510903

J. Marshall Osborn

Publication date: 1962

Full work available at URL: https://doi.org/10.2307/1993623

zbMATH Keywords

rings, modules, fields

Related Items (42)

Real commutative division algebras ⋮ Normal forms for the \(\mathcal G_2\)-action on the real symmetric \(7\times 7\)-matrices by conjugation ⋮ On the zeros of polynomials over arbitrary finite dimensional algebras ⋮ The non-orthogonal Cayley–Dickson construction and the octonionic structure of the E8-lattice ⋮ Octonions as Clifford-like algebras ⋮ Some new classes of division algebras ⋮ Some classes of pre-Hilbert algebras with norm-one central idempotent ⋮ On pre-Hilbert noncommutative Jordan algebras satisfying \(\|x^2\| = \|x\|^2\) ⋮ Isomorphieklassen vierdimensionaler quadratischer Divisionsalgebren über Hilbert-Körpern ⋮ Algebras with scalar involution revisited ⋮ Von-Neumann finiteness and reversibility in some classes of non-associative algebras ⋮ Similarity and consimilarity of elements in the real Cayley-Dickson algebras. ⋮ Color algebras and affine connections on \(S^ 6\) ⋮ On flexible quadratic algebras ⋮ Duplication methods for embeddings of real division algebras ⋮ A generalization of an algebra of Chevalley ⋮ Noncommutative Jordan Algebras of Capacity Two ⋮ Wild Pfister forms over Henselian fields, \(K\)-theory, and conic division algebras ⋮ A note on division algebras of dimension four ⋮ Automorphismengruppen achtdimensionaler lokalkompakter Quasikörper ⋮ How to obtain non-flexible quadratic algebras as mutation algebras of Hurwitz algebras ⋮ The degree of an eight-dimensional real quadratic division algebra is 1, 3, or 5 ⋮ Skew-symmetric identities of octonions ⋮ Some applications of nearfields ⋮ Degree three, four, and five identities of quadratic algebras ⋮ Monocomposition algebras ⋮ Structure theory for noncommutative Jordan \(H^ *\)-algebras ⋮ Eine Bemerkung zu quadratischen Divisionsalgebren ⋮ Halbeinfache quadratische Algebren und antikommutative Algebren mit assoziativen Bilinearformen ⋮ Kennzeichnung quasi-alternativer quadratischer Divisionsalgebren. (Characterization of quasi-alternative division algebras) ⋮ Varieties of algebras ⋮ Kennzeichnung quasi-alternativer quadratischer Divisionsalgebren ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Einige Bemerkungen über Divisionsalgebren ⋮ Zur Struktur der vierdimensionalen quadratischen Algebren ⋮ Real quadratic flexible division algebras ⋮ Imbedding of Mal'tsev algebras into alternative algebras ⋮ Liftings of dissident maps ⋮ On the variety determined by symmetric quadratic algebras ⋮ \((-1,-1)\)-balanced Freudenthal Kantor triple systems and noncommutative Jordan algebras ⋮ Quadratic division algebras revisited (Remarks on an article by J. M. Osborn)

Cites Work

• Unnamed Item
• Composition algebras and their automorphisms
• Linear algebras with associativity not assumed
• Power-associative rings
• Absolute-valued algebraic algebras

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