Products of several commutators in a Lie nilpotent associative algebra

Abstract

Abstract. Let F be a field of characteristic = 2, 3 and let A be a unital associative F -algebra. Define a left-normed commutator [a 1 , a 2 , . .. . , m k be positive integers such that ℓ of them are odd and k − ℓ of them are even. LetThe aim of the present note is to show that, for any positive integers m 1 , . . . , m k , in general,Recently Dangovski has proved that if m 1 , . . . , m k are any positive integers then, in general,