Third-power associative absolute valued algebras with a nonzero idempotent commuting with all idempotents
Cuenca Mira, José Antonio (Universidad de Málaga. Departamento de Álgebra, Geometría y Topología)
Data: |
2014 |
Resum: |
This paper deals with the determination of the absolute valued algebras with a nonzero idempotent commuting with the remaining idempotents and satisfying x2x = xx2 for every x. We prove that, in addition to the absolute valued algebras R, C, H, or O of the reals, complexes, division real quaternions or division real octonions, one such absolute valued algebra A can also be isometrically isomorphic to some of the absolute valued algebras C. H or O, obtained from C, H, and O by imposing a new product defined by multiplying the conjugates of the elements. In particular, every absolute valued algebra having the above properties is finite-dimensional. This generalizes some well known theorems of Albert, Urbanik and Wright, and El-Mallah. |
Drets: |
Tots els drets reservats. |
Llengua: |
Anglès |
Document: |
Article ; recerca ; Versió publicada |
Matèria: |
Absolute valued algebra ;
Idempotent ;
Division algebra ;
Third-power associativity ;
Pairwise commuting elements |
Publicat a: |
Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 469-484, ISSN 2014-4350 |
Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287186
DOI: 10.5565/PUBLMAT_58214_23
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