Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T10:33:46.040Z Has data issue: false hasContentIssue false
  • English
  • Français

Logarithmetics of Finite Quasigroups (I)

Published online by Cambridge University Press:  20 January 2009

Helen Popova
Helen Popova
Affiliation:
Depaetment of Mathematics, University of Abeedeen.
Rights & Permissions [Opens in a new window]

Extract

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.

The study of non-associative algebras led to the investigation of identities connecting powers of elements of such algebras. Thus Etherington1 (1941, 1949, 1951) introduced the concept of the logarithmetic of an algebra, defining it roughly as “ the arithmetic of the indices of the general element”.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 2 , November 1954 , pp. 74 - 81
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

1 Etherington, I. M. H., “Some non-associative algebras in which the multiplication of indices is commutative”, Journal London Math. Soc., 16 (1941), 48–55CrossRefGoogle Scholar; “Nonassociative arithmetics” Proc. Roy. Soc. Edinburgh (A), 62 (1949), 442–453Google Scholar; “Noncommutative train algebras of rank 2 and 3”, Proc. London Math. Soc. (2), 52 (1951), 241–252.Google Scholar

2 Murdoch, D. C., “Quasigroups which satisfy certain generalised associative laws” American J. of Math., 61 (1939), 509–522.CrossRefGoogle Scholar

3 Hausmann, B. A. and Ore, O., “Theory of quasigroups” American J. of Math., 59 (1937), 983–1004.CrossRefGoogle Scholar

1 Etherington, I. M. H., “On non-associative combinations”, Proc. Roy. Soc. Edinburgh. 69 (1939), 153–162.Google Scholar