Residually Finite Varieties of Nonassociative Algebras

Abstract

Abstract We prove that if 𝒱 is a residually finite variety of nonassociative algebras over a finite field, and the enveloping algebra of each finite member of 𝒱 is finitely generated as a module over its center, then 𝒱 is generated by a single finite algebra. Key Words: Lie algebraNonassociative algebraResidually finiteSubdirectly irreducibleVariety2000 Mathematics Subject Classification: Primary 17A60Secondary 08B26, 17B05 Notes Communicated by A. Olshanskii.