Abstract
We use a computer to verify that the ideal N of all weight zero elements of any (not necessarily finite dimensional) Bernstein algebra is solvable of index ≤4. We also use a computer to verify that N 2 is nilpotent of index ≤9. We give three examples of Bernstein algebras which show that various hypotheses like finite dimensionality, finitely generatedA 2 = A, are separately not enough to force N to be nilpotent.
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