Boolean structures and the genetic code: some comments
Abstract
This is a paper of divulgative character in which our aim is to study some classical results about boolean structures from the viewpoint of P. Halmos [4]. In particular, we are interested in the proofs of two fundamental isomorphism theorems of boolean algebras. Also, we discuss a recent and illustrative representation of the
RNAm in terms of the boolean algebra Z62[3].
Visitas al artículo
Downloads
References
Betz, C.: “Introducción a la Teoría de la Medida e Integración”. Imprenta Universitaria-UCV. Caracas, Venezuela. (1992).
Boole, G.: “An investigation of the laws of thought”. Publications, Inc. Cork, Irlanda. (1854).
Grau, R., Chavez, M., Sanchez, R., Morgado, E., Casas, G., Bonet, I.: “Boolean Algebraic Structures of the Genetic Code: Possibilities of Applications”. En Knowledge Discovery and Emergent Complexity in Bioinformatics. First International Workshop, KDECB 2006, Ghent, Belgium, May 10, 2006. Revised Selected Papers. Karl Tuyls et al. Editors. Lecture Notes in Computer Sciences, Vol. 4366, 10-21, (2007).
Halmos, P.: “Lectures on Boolean Algebras”. Springer-Verlag, New York, USA. (1974).
Halmos, P.: “The Legend of John Von Neumann”. Amer. Math. Montly, 80 (4), 382-394, (1973).
Herstein, I. N.: “Álgebra Abstracta”. Grupo Editorial Iberoame´rica, S.A. Distrito Capital, Me´xico. (1988).
Huntington, E. V.: “New sets of independent postulates for the algebra of logic” , Trans. Amer. Math. Soc. 35, 274-304, (1933).
Peinado, R. E.: “Elementos nilpotentes e idempotentes en los anillos Zn”, Revista Matem´atica Hispanamericana, 26, No. 1-2, (1966).
Royden, H. L.: “Real Analysis”. Prentice Hall. London, Inglaterra. (1995).
Shannon, C. E.: “A Symbolic Analysis of Relay and Switching Circuits”, Trans. AIEE, 57 (12), 713-723, (1938).
Turing, A.: “On computable numbers, with an application to the Entscheidungsproblem”, Proc. Lond. Math. Soc. Series 2, 42, 230-265, (1936-7). Errata aparecida en Series 2, 43, 544-546, (1937).
Vladimirov, D. A.: “Boolean Algebras in Analysis”. Kluwer Academic Publishers. Dordrecht, Netherlands. (2002).