Solvability of the ideal of all weight zero elements in bernstein algebras

摘要

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 #x2264;4. We also use a computer to verify thatN2is nilpotent of index #x2264;9. We give three examples of Bernstein algebras which show that various hypotheses like finite dimensionality, finitely generatedA2=A, are separately not enough to forceNto be nilpotent.