When is ℝ 2 a Division Algebra?

DOI10.2307/2323281zbMath0524.17001OpenAlexW2320966443MaRDI QIDQ3037632

L. D. Kugler, Steven C. Althoen

Publication date: 1983

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2323281

zbMATH Keywords

classificationidempotentsbasis multiplication schemesquasi-commutative algebrasquasi-complex algebrastwo-dimensional nonassociative real division algebras

Mathematics Subject Classification ID

Nonassociative division algebras (17A35)

Related Items (15)

Real commutative division algebras ⋮ Frobenius algebra with relaxed associativity constraint ⋮ Four-dimensional real division algebras with few derivations ⋮ Real division algebras with a nontrivial reflection ⋮ Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras ⋮ The classification of two-dimensional nonassociative algebras ⋮ Duplication methods for embeddings of real division algebras ⋮ On a theorem by Hopf ⋮ Ternary derivations of finite-dimensional real division algebras ⋮ On two-dimensional power associative algebras over algebraically closed fields and \(\mathbb R\) ⋮ Complex Structures in Real Algebras. I. Two-Dimensional Commutative Case ⋮ CLASSIFICATION, AUTOMORPHISM GROUPS AND CATEGORICAL STRUCTURE OF THE TWO-DIMENSIONAL REAL DIVISION ALGEBRAS ⋮ Elementary Derivations of the Euclidean Hurwitz Algebras Adapted from Gadi Moran’s last paper ⋮ Polynomial invariants and moduli of generic two-dimensional commutative algebras ⋮ Real quadratic flexible division algebras

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