IMCS/Publications/BASM/Issues/BASM n.2 (12), 1993/

Independence and nilpotency in algebras. (Russian)

Authors: Chekanu G. P., Cojuhari Elena


In the work the following theorem about the independence is proved: if the word $w$ is maximal among all nonzero products of length not exceeding $n$ and all the ends of $w$ are nilpotent, then all the beginning a linear-independent. Some applications of this theorem are pointed out. Particularly, the truth of I.Shestakov's conjecture is confirmed, another proof of Wedderburn theorem about the nilpotency of a finitedimensional algebra with a nil bases is given. This proof does not use classic structure results.

Institutul de Matematica Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău MD-2028, Moldova