In this work we gave some general statements about independence in algebras. This permitted for us to confirm the truth of I. Shestakov's conjecture and to obtain the extension of classical Shirshov's theorem about nilpotence and finitedimensionality of algebras.
Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău, MD-2028 Moldova