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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 ; publishedVersion
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 0214-1493

DOI: 10.5565/PUBLMAT_58214_23

16 p, 332.2 KB

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