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Modular Bernstein algebras. (English) Zbl 0794.17018
The first part of this paper generalizes some results – obtained by the author in previous papers about genetic Bernstein algebras, to Bernstein algebras that are not necessarily genetic; first, modular non-trivial Bernstein algebras and exclusive algebras are studied. Then the natural question is if all modular Bernstein algebras are necessarily genetic; the answer is no if the algebra is built on an arbitrary field, and the author gives an example of such a case.
The following theorem is proved: Any modular Bernstein algebra over an algebraically closed field of characteristic different from two is genetic.

17D92 Genetic algebras
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