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An equivalence in generalized almost-Jordan algebras

dc.creatorGuzzo Jr., Henrique
dc.creatorLabra, Alicia
dc.date2017-03-23
dc.identifierhttp://www.revistaproyecciones.cl/article/view/1325
dc.identifier10.4067/S0716-09172016000400011
dc.descriptionIn this paper we work with the variety of commutative algebras satisfying the identity β((x2y)x — ((yx)x)x) +γ(x3y — ((yx)x)x) = 0, where β, γ are scalars.    They are called generalized almost-Jordanalgebras. We prove that this variety is equivalent to the variety of commutative algebras satisfying (3β + γ)(Gy(x,z,t) — Gx(y,z,t)) + (β + 3γ)(J(x,z,t)y — J(y,z,t)x) = 0, for all x,y,z,t ∈ A, where J(x,y,z) = (xy)z+(yz)x+(zx)y and Gx(y,z,t) = (yz,x,t)+(yt,x,z)+ (zt,x,y). Moreover, we prove that if A is a commutative algebra, then J (x, z, t)y = J (y, z, t)x, for all x, y, z, t ∈ A, if and only if A is a generalized almost-Jordan algebra for β= 1 and γ = —3, that is, A satisfies the identity (x2y)x + 2((yx)x)x — 3x3y = 0 and we study this identity. We also prove that if A is a commutative algebra, then Gy(x,z,t) = Gx(y,z,t), for all x,y,z,t ∈ A, ifand only if A is an almost-Jordan or a Lie Triple algebra.es-ES
dc.formatapplication/pdf
dc.languagespa
dc.publisherUniversidad Católica del Norte.es-ES
dc.relationhttp://www.revistaproyecciones.cl/article/view/1325/1036
dc.rightsDerechos de autor 2016 Proyecciones. Journal of Mathematicses-ES
dc.rightshttps://creativecommons.org/licenses/by-nc/4.0/es-ES
dc.sourceProyecciones. Journal of Mathematics; Vol 35 No 4 (2016); 505-519en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 35 Núm. 4 (2016); 505-519es-ES
dc.source0717-6279
dc.source0716-0917
dc.titleAn equivalence in generalized almost-Jordan algebrases-ES
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typeArtículo revisado por pareses-ES


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