A short characterization of the octonions
| Autor: | Yoav Segev, Erwin Kleinfeld |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Ring (mathematics) Algebra and Number Theory Mathematics::Number Theory Commutator (electric) Associator Group Theory (math.GR) Mathematics - Rings and Algebras Characterization (mathematics) law.invention Mathematics::Algebraic Geometry Rings and Algebras (math.RA) law FOS: Mathematics Octonion algebra Primary: 17D05 Secondary: 17A35 Mathematics - Group Theory Additive group Mathematics |
| Zdroj: | Communications in Algebra. 49:5347-5353 |
| ISSN: | 1532-4125 0092-7872 |
| Popis: | In this paper we prove that if $R$ is a proper alternative ring whose additive group has no $3$-torsion and whose non-zero commutators are not zero-divisors, then $R$ has no zero-divisors. It follows from a theorem of Bruck and Kleinfeld that if, in addition, the characteristic of $R$ is not $2,$ then the central quotient of $R$ is an octonion division algebra over some field. We include other characterizations of octonion division algebras and we also deal with the case where $(R,+)$ has $3$-torsion. There are better results and better proofs in this final version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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