Dibaric algebras

• Couto, Maria Aparecida ^[1] ; Gutiérrez Fernández, Juan C.
  1. [1] Universidade Federal do Rio Grande do Norte

     Universidade Federal do Rio Grande do Norte

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 19, Nº. 3, 2000, págs. 249-269
• Idioma: inglés
• DOI: 10.4067/S0716-09172000000300003
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • Citas [1] R. Costa and H. Jr Guzzo, Indecomposable baric algebras, Linear Algebra Appl. 183, pp. 223-236, (1993).
  • [2] R. Costa and H. Jr Guzzo, Indecomposable baric algebras II, Linear Algebra Appl. 196, pp. 233-242, (1994).
  • [3] I.M.H. Etherington, On non-associative combinations, Proc. Edinb. Math. Soc. 59, pp. 153-162, (1939).
  • [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).