Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-13T08:22:47.054Z Has data issue: false hasContentIssue false
  • English
  • Français

The nuclei of non-associative division algebras

Published online by Cambridge University Press:  24 October 2008

D. Rees
D. Rees
Affiliation:
The UniversityManchester
Get access Rights & Permissions [Opens in a new window]

Extract

The results of this paper have as their background two concepts fundamental in the theory of non-associative algebras (i.e. algebras in which the associative law of multiplication is not assumed). These concepts are:

(1) Isotopy,

(2)The three nuclei λ, μ, ρ of an algebra .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 1 , January 1950 , pp. 1 - 18
Copyright
Copyright © Cambridge Philosophical Society 1950

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

(1)Albert, A. A.Non-associative algebras. I. Fundamental concepts and isotopy. Ann. Math. 43 (1942), 685–707.CrossRefGoogle Scholar
(2)Albert, A. A. Structure of algebras. American Math. Soc. Colloquium Publications, 24 (New York, 1939).Google Scholar
(3)Bruck, R. H.Contribution to the theory of loops: Trans. American Math. Soc. 60 (1946), 245–354.CrossRefGoogle Scholar
(4)Bruck, R.Some results in the theory of linear non-associative algebras. Trans. American Math. Soc. 56 (1944), 141–199.CrossRefGoogle Scholar
(5)Eilenberg, S. and Maclane, S.Cohomology and Galois theory. I. Normality of algebras and Teichmuller's cocycle. Trans. American Math. Soc. 64 (1948), 1–20.Google Scholar
(6)Etherington, I. M. H.Transposed algebras. Proc. Edinburgh Math. Soc. (2), 7 (1945), 104–21.CrossRefGoogle Scholar
(7)Jacobson, N. Theory of rings. American Math. Soc. Math. Surveys, no. 2 (New York, 1943).Google Scholar
(8)Schönhardt, E.Über lateinische Quadraten und Unionen. J. Math. 163 (1930), 183–230.Google Scholar