Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T00:47:06.149Z Has data issue: false hasContentIssue false
  • English
  • Français

E-Ideals in baric algebras: basic properties

Published online by Cambridge University Press:  20 January 2009

A. Catalan ,
C. Mallol  and
R. Costa
A. Catalan
Affiliation:
Depto de Matematica, Universidad de la Frontera, Casilla 54-D, Temuco, ChileE-mail address:[email protected], [email protected]
C. Mallol
Affiliation:
Depto de Matematica, Universidad de la Frontera, Casilla 54-D, Temuco, ChileE-mail address:[email protected], [email protected]
R. Costa
Affiliation:
Instituto de Matemática e Estatistica-USP, Caixa Postal 66.281-Agência Cidade de Sāo Paulo, 05389-970-Sāo Paulo, BrasilE-mail address:[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this work we introduce the notion of E-ideal, generalizing I. M. H. Etherington's idea. We study the general characteristics of the lattice of E-ideals in baric algebras, and some properties inherited from an arithmetic of train polynomials.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 3 , October 1997 , pp. 491 - 503
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

REFERENCES

1.Cortes, T. and Montaner, F., On the structure of Bernstein algebras, Proc. London Math. Soc., to appear.Google Scholar
2.Costa, R., Principal train algebras of rank 3 and dimension ≤ 5, Proc. Edinburgh Math. Soc. 33 (1990), 61–70.CrossRefGoogle Scholar
3.Costa, R. and Guzzo, H. Jr., Indecomposable baric algebras, Linear Alg. Appl. 183 (1993), 223–236.CrossRefGoogle Scholar
4.Costa, R. and Guzzo, H. Jr., Indecomposable baric algebras II, Linear Alg. Appl. 196 (1994), 233–242.CrossRefGoogle Scholar
5.Etherington, I. M. H., Genetic algebras, Proc. Royal Soc. Edinburgh 59 (1939), 242–258.CrossRefGoogle Scholar
6.Guzzo, H. Jr., Embedding nil algebras in train algebras, Proc. Edinburgh Math. Soc. 37 (1994), 463–470.CrossRefGoogle Scholar
7.Guzzo, H. Jr., The Peirce decomposition for commutative train algebras, Comm. Algebra 22 (1994), 5745–5757.Google Scholar
8.Ljubich, I., Mathematical Structures in Population Genetics (Biomathematics, 22, Springer, 1992).CrossRefGoogle Scholar
9.Martinez, C., Isomorphisms of Bernstein algebras, J. Algebra 160 (1993), 419–423.CrossRefGoogle Scholar
10.Micali, A. and Ouattara, M., Dupliqueé d'une algèbre et le théorème d'Etherington, Linear Alg. Appl. 153 (1991), 193–207.CrossRefGoogle Scholar
11.Osborn, J. M., Varieties of algebras, Adv. Math. 8 (1972), 163–369.CrossRefGoogle Scholar
12.Ouattara, M., Sur les T-algèbres de Jordan, Linear Alg. Appl. 144 (1991), 11–21.CrossRefGoogle Scholar
13.Walcher, S., Algebras which satisfy a train equation for the first three plenary powers, Arch. Math. 56 (1991), 547–551.CrossRefGoogle Scholar
14.Worz, A., Algebras in Genetics (Lecture Notes in Biomathematics, 36, 1980).CrossRefGoogle Scholar