An equivalence in generalized almost-Jordan algebras
| dc.creator | Guzzo Jr., Henrique | es |
| dc.creator | Labra, Alicia | es |
| dc.date | 2017-03-23 | |
| dc.date.accessioned | 2025-10-06T15:05:04Z | |
| dc.date.available | 2025-10-06T15:05:04Z | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1325 | |
| dc.identifier | 10.4067/S0716-09172016000400011 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/255495 | |
| dc.description | In 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 |
| dc.format | application/pdf | |
| dc.language | spa | |
| dc.publisher | Universidad Católica del Norte. | en |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1325/1036 | |
| dc.rights | Copyright (c) 2016 Proyecciones. Journal of Mathematics | en |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | en |
| dc.source | Proyecciones (Antofagasta); Vol. 35 No. 4 (2016); 505-519 | en |
| dc.source | Proyecciones. Revista de Matemática; Vol. 35 Núm. 4 (2016); 505-519 | es |
| dc.source | 0717-6279 | |
| dc.source | 10.22199/issn.0717-6279-2016 | |
| dc.title | An equivalence in generalized almost-Jordan algebras | es |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion |
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Proyecciones: Journal of Mathematics
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