The problem of the existence of a finite basis of identities for a variety of associative algebras over a field of characteristic zero was formulated by Specht in 1950. We say that a variety of algebras has the Specht property if any of its subvariety has a finite basis of identities. In 1988, A. Kemer proved that the variety of associative algebras over a field of characteristic zero has the Specht property. Specht’s problem has been studied for many well-known varieties of algebras, such as Lie algebras, alternative algebras, right-alternative algebras, and Novikov algebras. An algebra is called right-symmetric if it satisfies the identity (a,b,c) = (a,c,b) where (a,b,c) = (ab)c − a(bc) is the associator of a, b, c. The talk is devoted to the Specht problem for the variety of right-symmetric algebras. It is proved that the variety of right-symmetric algebras over an arbitrary field does not satisfy the Specht property.
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