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Solvability of the ideal of all weight zero elements in bernstein algebras |
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| Authors: | Irvin Roy Hentzel David Pokrass Jacobs Luiz Antonio Peresi Sergei Robertovich Sverchkov |
| Institution: | 1. Department of Mathematics , Iowa State University , Ames, Iowa, 50011, USA;2. Department of Computer Science , Clemson University , Clemson, SC, 29634-1906, USA;3. Departamento de Matemática , Universidade de Sao Paulo , C.P. 20570 (Ag. Jardim Paulistano), Sao Paulo, 01452-990, Brazil |
| 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. |
| Keywords: | Division rings Orderings of higher level Signatures Valuations |