Dibaric algebras

Authors

  • Maria Aparecida Couto Universidade Federal do Río Grande do Norte.
  • Juan C. Gutiérrez Fernández Universidade de Sao Paulo.

DOI:

https://doi.org/10.4067/S0716-09172000000300003

Keywords:

Nonassociative algebras, baric algebras, genetic algebras, dibaric algebras, álgebra no asociativa, álgebras báricas, álgebras genéticas, álgebras dibáricas.

Abstract

Here we give basic properties of dibaric algebras which are motivated by genetic models. Dibaric algebras are not associative and they have a non trivial homomorphism onto the sex differentiation algebra. We define first join of dibaric algebras next indecomposable dibaric algebras. Finally, we prove the uniqueness of the decomposition of a dibaric algebra, with semiprincipal idempotent, as the join of indecomposable dibaric algebras.

Author Biographies

Maria Aparecida Couto, Universidade Federal do Río Grande do Norte.

Departamento de Matemática.

Juan C. Gutiérrez Fernández, Universidade de Sao Paulo.

Instituto de Matemática e Estatística,Departamento de Matemática.

References

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[4] P. Holgate, Genetic Algebras associated with sex linkage, Proc. Edinb. Math. Soc. 17, pp. 113-120, (1970).

[5] Y. Lyubich, Mathematical Structure in Populations Genetics, Springer-Verlag, (1983).

[6] M. Lynn Reed, Algebraic structures of genetic inheritance, Bull. Amer. Math. Soc (N. S.) 34, No. 2, pp. 107-131, (1997).

[7] A. Wörz-Busekros, Algebras in Genetics, Springer-Verlag vol. 36, (1980).

[8] A. Wörz-Busekros, The zygotic algebra for sex linkage, J. Math. Biol. 1, pp. 37-46, (1974).

[9] A. Wörz-Busekros, The zygotic algebra for sex linkage II, J. Math. Biol. 2, pp. 359-371, (1975).

Published

2017-06-14

How to Cite

[1]
M. A. Couto and J. C. Gutiérrez Fernández, “Dibaric algebras”, Proyecciones (Antofagasta, On line), vol. 19, no. 3, pp. 249-269, Jun. 2017.

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