Identités Multilinéaires de Degré 4 pour les Algèbres de Bernstein et de Mutation Non Commutatives

REFERENCES

• Etherington , I. M. H. ( 1940 ). Commutative train algebras of rank 2 and 3 . J. London Math. Soc. 15 : 136 – 149 . Corrigendum, ibid. 20 (1945): 238 .
   Google Scholar
• Etherington , I. M. H. ( 1951 ). Non-commutative train algebras of rank 2 and 3 . Proc. London Math. Soc. 52 : 241 – 252 .
   Google Scholar
• Baeza-Vega , R. , Costa , R. ( 1994 ). Shape identities in genetic algebras. II . Algebras Groups Geom. 11 : 379 – 395 .
   Google Scholar
• Baeza-Vega , R. , Correa , I. , Costa , R. , Peresi , L. A. ( 1997 ). Shape identities in Bernstein algebras . Comm. Algebra 25 : 2659 – 2679 .
   Web of Science ®Google Scholar
• Bernad , J. , Gonzalez , S. , Martinez , C. , Iltyakov , A. V. ( 1997 ). On identities of baric algebras and superalgebras . J. Algebra 197 : 385 – 408 .
   Web of Science ®Google Scholar
• Bernad , J. , Gonzalez , S. , Martinez , C. , Iltyakov , A. V. ( 1998 ). Polynomial Identities of Bernstein algebras of small dimension . J. Algebra 207 : 664 – 681 .
   Web of Science ®Google Scholar
• Bremner , M. R. ( 2005 ). Jordan algebras arising from intermolecular recombination . SIGSAM Bull. 39 : 106 – 117 .
   Google Scholar
• Bremner , M. R. , Hentzel , I. R. , Peresi. L. A. ( 2005 ). Dimension formulas for the free nonassociative algebra . Comm. Algebra 33 : 4063 – 4081 .
   Web of Science ®Google Scholar
• Bremner , M. R. , Piao , Y. , Richards , S. W. ( 2009 ). Polynomial identities for Bernstein algebras of simple mendelian inheritance . Comm. Algebra 37 : 3438 – 3455 .
   Web of Science ®Google Scholar
• Correa , I. , Hentzel , I. R. , Peresi , L. A. ( 1994 ). Minimal identities of Bernstein algebras . Algebras Groups Geom. 11 : 181 – 199 .
   Google Scholar
• Costa , R. ( 1995 ). Shape identities in genetic algebras . Linear Algebra Appl. 214 : 119 – 131 .
   Google Scholar
• Labra , A. , Reyes , C. ( 2001 ). On polynomial identities on train algebras of rank 3. East-West . J. Math. 3 : 195 – 200 .
   Google Scholar
• Lyubich , Yu. I. ( 1992 ). Mathematical Structures in Population Genetics . Biomathematics, 22 . Berlin : Springer-Verlag .
   Google Scholar
• Mallol , C. , Varro , R. ( 1994 ). Les Algèbres de Mutation . Non associative algebras and its applications . Amsterdam : Kluwer Academic Pub. , pp. 245 – 251 .
   Google Scholar
• Mallol , C. , Varro , R. ( 2000 ). Conditions d'existence d'une loi de Hardy-Weinberg périodique dans les populations sélectivement neutres. Nonassociative algebra and its applications (São Paulo, 1998) Lecture Notes in Pure and Appl. Math. Vol. 211 . New York : Dekker , pp. 439 – 446 .
   Google Scholar
• Peresi , L. A. ( 1992 ). Minimal polynomial identities of Bernstein algebras. A computer approach. XII School of Algebra, Part I (Portuguese) (Diamantina, 1992) . Mat. Contemp. 6 : 219 – 224 .
   Google Scholar
• Peresi , L. A. ( 1994 ). Minimal polynomial identities of baric algebras. Non-associative algebra and its applications (Oviedo, 1993). Math. Appl., 303 . Dordrecht : Kluwer Acad. Publ. , pp. 323 – 329 .
   Google Scholar
• Peresi , L. A. ( 2004 ). A basis of identities for Bernstein algebras . Int. J. Math. Game Theory Algebra 14 : 179 – 188 .
   Google Scholar
• Sverchkov , S. R. ( 2009 ). Structure and representations of Jordan algebras arising from intermolecular recombination . Algebras, Representations and Applications. Contemporary Mathematics AMS 483 : 261 – 285 .
   Google Scholar
• Wörz-Busekros , A. ( 1980 ). Algebras in Genetics . Lecture Notes in Biomathematics, Vol. 36 . New York : Springer-Verlag .
   Google Scholar
• Zhevlakov , K. A. , Slin'ko , A. M. , Shestakov , I. P. ( 1982 ). Rings That are Nearly Associative . Pure and Applied Mathematics, 104 . New York-London : Academic Press, Inc .
   Google Scholar
• Communicated by A. Elduque.
   Google Scholar