Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-02-06T10:26:27.305Z Has data issue: false hasContentIssue false
  • English
  • Français

XXIII.—Genetic Algebras

Published online by Cambridge University Press:  15 September 2014

I. M. H. Etherington
I. M. H. Etherington
Affiliation:
Mathematical Institute, University of Edinburgh
Get access

Extract

Two classes of linear algebras, generally non-associative, are defined in § 3 (baric algebras) and § 4 (train algebras), and the process of duplication of a linear algebra in § 5. These concepts, which will be discussed more fully elsewhere, arise naturally in the symbolism of genetics, as shown in §§ 6–15. Many of their properties express facts well known in genetics; and the processes of calculation which are fundamental in many problems of population genetics can be expressed as manipulations in the genetic algebras. In cases where inheritance is of a simple type (e.g. §§ 10–13, 15) this constitutes a new point of view, but perhaps amounts to little more than a change of notation as compared with existing methods. §14, however, indicates the possibility of generalisations which would seem to be impossible by ordinary methods.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 59 , 1940 , pp. 242 - 258
Copyright
Copyright © Royal Society of Edinburgh 1940

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References to Literature

Aitken, A. C., 1935. “The normal form of compound and induced matrices,” Proc. Lond. Math. Soc. (2), vol. xxxviii, pp. 354–376.CrossRefGoogle Scholar
Dickson, L. E., 1914 (reprinted 1930). Linear algebras, Cambridge Tract, No. 16.Google Scholar
Etherington, I. M. H., 1939. “On non-associative combinations,” Proc. Roy. Soc. Edin., vol. lix, pp. 153–162.Google Scholar
Geppert, H., and Koller, S., 1938. Erbmathematik, Leipzig.Google Scholar
Glivenko, V., 1936. “Algèbre mendelienne,” Moscow Acad. Sci. C.R., vol. iv, pp. 385–386.Google Scholar
Haldane, J. B. S., 1918. “The combination of linkage values,” Journ. Gen., vol. viii, pp. 299–309.Google Scholar
Haldane, J. B. S., 1930. “Theoretical genetics of autopolyploids,” Journ. Gen., vol. xxii, pp. 359–372.CrossRefGoogle Scholar
Jennings, H. S., 1935. Genetics, London.Google Scholar
Wedderburn, J. H. M., 1908 (a). “On hypercomplex numbers,” Proc. Lond. Math. Soc. (2), vol. vi, pp. 77–118.CrossRefGoogle Scholar
Wedderburn, J. H. M., 1908 (b). “On certain theorems in determinants,” Proc. Edin. Math. Soc. (1), vol. xxvii, pp. 67–69.Google Scholar