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Algebraic structure of genetic inheritance. (English) Zbl 0876.17040
The object of this survey article is to spread one of the most interesting applications of the nonassociative algebra (the genetic algebra) and to present its basis, methods, and recent advances. The author includes a genetic motivation where the necessary language of the biology is introduced. Next, he shows the way in which the genetic information inherited through the generations becomes natural nonassociative algebraic structures. The paper contains a general view of the most important classes of nonassociative algebras with genetic significance (baric algebras, train algebras, Bernstein algebras, ...) which are treated in the following sections. The work finishes with sections devoted to applications and conclusions and an abundant set of references on genetic algebra.
The author remarks in her conclusions that only very few American mathematicians are involved in current work being done in the field and anticipates that “... this article will open an avenue for future discussion and research into this fascinating class of nonassociative algebras and their relationship to the science of genetic inheritance” (sic).

MSC:
17D92 Genetic algebras
92D10 Genetics and epigenetics
17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras
92-02 Research exposition (monographs, survey articles) pertaining to biology
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