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Algebra Logika, 2010 Volume 49, Number 3, Pages 388–423 (Mi al446)

This article is cited in 16 papers

Isotopes of prime $(-1,1)$- and Jordan algebras

S. V. Pchelintsev

Finance Academy under the Government of the Russian Federation, Moscow, Russia

Abstract: We deal with adjoint commutator and Jordan algebras of isotopes of prime strictly $(-1,1)$-algebras. It is proved that a system of identities of the form $[x_1,x_2,x_2,x_3,\dots,x_n]$ for $n=2,\dots,5$ is discernible on isotopes of prime $(-1,1)$-algebras. Also it is shown that adjoint Jordan algebras for suitable isotopes of prime $(-1,1)$-algebras may possess distinct sets of identities. In particular, isotopes of a prime Jordan monster have different sets of identities in general.

Keywords: right alternative algebra, strictly $(-1,1)$-algebra, Jordan algebra, prime algebra, isotope, homotope, identity, Lie nilpotence.

UDC: 512.554

Received: 09.09.2009


 English version:
Algebra and Logic, 2010, 49:3, 262–288

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