Il’tyakov, A. V. Finiteness of the basis of identities of a finitely generated alternative PI-algebra over a field of characteristic zero. (Russian) Zbl 0749.17043 Sib. Mat. Zh. 32, No. 6(190), 61-76 (1991). Since the famous result of A. R. Kemer [Algebra Logic 26, 362-397 (1987); translation from Algebra Logika 26, 597-641 (1987; Zbl 0646.16016)] who established the Specht property for associative algebras over a field of characteristic zero significant developments of his method have been made. A. Ya. Vajs and E. I. Zel’manov [Sov. Math. 33, No. 6, 38-47 (1990); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1989, No. 6, 42-51 (1989; Zbl 0679.17013)] extended Kemer’s result to finitely generated Jordan algebras.The author of the paper under review improved the technique of Kemer in two preprints [On varieties of representations of Lie algebras (Russian) (Akad. Nauk SSSR, Sib. Div., Inst. Math., Novosibirsk, Preprint No. 9) (1991) and Specht’s property of varieties of PI-representations of finitely generated Lie algebras over a field of characteristic zero (Russian) (Akad. Nauk SSSR, Sib. Div., Inst. Math., Novosibirsk, Preprint No. 10) (1991)]. He established, in particular, that every finite dimensional Lie algebra is Spechtian.Now following the scheme of Kemer and of his preprints the author proves that every finitely generated alternative PI-algebra is Spechtian (over a field of characteristic zero). Reviewer: P.Koshlukov (Sofia) Cited in 1 ReviewCited in 4 Documents MSC: 17D05 Alternative rings 17A50 Free nonassociative algebras 16R10 \(T\)-ideals, identities, varieties of associative rings and algebras 16R99 Rings with polynomial identity Keywords:polynomial identities; \(T\)-ideals; \(T\)-spaces; finite bases of identities; Specht property; characteristic zero; alternative PI-algebra Citations:Zbl 0646.16016; Zbl 0679.17013 × Cite Format Result Cite Review PDF Full Text: EuDML