Abstract
In this note we show that for finite-dimensional Bernstein algebras over a field of characteristic different from 2: 1. (1) The principal nilpotency of an element implies its strong nilpotency. 2. (2) If Ker(ω) is a nil algebra, then it is a train algebra. 3. (3) Every train algebra of dimension n ⩽ 5 is special train algebra, and that is a best possible result.
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