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On the genetic property of Bernstein algebras. (English. Russian original) Zbl 0643.17017
Sov. Math., Dokl. 35, No. 3, 489-492 (1987); translation from Dokl. Akad. Nauk SSSR 194, No. 1, 27-30 (1987).
The author proves a conjecture of Lyubich which says that if a Bernstein algebra B satisfies the condition B $$2=B$$ then B is a genetic algebra. In proving the theorem use is made of spaces with a ternary operation having special properties.
Reviewer: H.Gonshor

##### MSC:
 17D92 Genetic algebras 17A30 Nonassociative algebras satisfying other identities
##### Keywords:
Bernstein algebra; genetic algebra; ternary operation