×

zbMATH — the first resource for mathematics

Multi-algebra duplication. (English) Zbl 0658.92015
The aim of this paper is to use multi-algebra duplication to simplify the proofs of J. Lopez-Sanchez, and A. Perez de Vargas [Bull. Math. Biol. 47, 771-782 (1985; Zbl 0586.92016)], and to show that this idea can be usefully applied to other situations. The author starts, however, with a brief, but very lucid introduction to some of the basic algebraic ideas in genetics - this should prove very useful to readers not very familiar with this subject. For a full account of algebra in genetics he rightly refers the reader to A. Wörz-Busekros [Algebras in genetics. Lect. Notes in Biomathematics 36 (1980; Zbl 0431.92017)].
Multi-algebra duplication of two algebras having a common basis is defined in terms of the duplication of either algebra [see the author’s paper, Proc. Edinburgh Math. Soc., II. Ser. 17, 289-298 (1971; Zbl 0247.92002)], and his two main theorems are concerned with subalgebras of such a duplication, and the train roots. [In Theorem 1, the first lower case “c” should be replaced by an upper case “C”.]
Reviewer: E.W.Wallace

MSC:
92D10 Genetics and epigenetics
17D92 Genetic algebras
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Gonshor, H.: Special train algebras arising in genetics. Proc. Edinb. Math. Soc. 12, 41-53 (1980) · Zbl 0249.17003
[2] Gonshor, H.: Special train algebras arising in genetics II. Proc. Edinb. Math. Soc. 14, 333-338 (1965) · Zbl 0139.03102
[3] Gonshor, H.: Contributions to genetic algebras. Proc. Edinb. Math. Soc. 17, 289-298 (1977) · Zbl 0247.92002
[4] Gonshor, H.: Contributions to genetic algebras II. Proc. Edinb. Math. Soc. 18, 273-279 (1973) · Zbl 0272.92012
[5] Lopez-Sanchez, J., Perez de Vargas, A.: Zygotic algebra for two linked loci with sexually different recombination rates. Bull. Math. Biol. 47, 771-782 (1985) · Zbl 0586.92016
[6] Worz-Busekros, A.: Algebras in genetics. Lect. Notes Biomath. 36. Berlin Heidelberg New York: Springer 1980 · Zbl 0431.92017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.