E-resources
Peer reviewed
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Eroğlu, Münevver Pınar
Journal of algebra, 03/2022, Volume: 594Journal Article
Let A be a unital algebra over a field of characteristic different from 2. The main goal of this work is to characterize higher commutators of A. In particular, we show that if H is a noncommutative higher commutator of A and contains the unity, then H is equal to either A or A,A. As a result, we prove that if there exist x,y∈A such that 1=x,y, then the only higher commutators of A are A and A,A. We also consider the structure of noncommutative Lie ideals of the form U,A, where U is a Lie ideal of A, and show that if L=U,A is noncommutative and contains the unity, then L=A,A and A,A⊆U.
