Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T01:32:02.739Z Has data issue: false hasContentIssue false
  • English
  • Français

An Extension of the Class of Alternative Rings

Published online by Cambridge University Press:  20 November 2018

D. L. Outcalt
D. L. Outcalt*
Affiliation:
Claremont Men's College, Claremont, California
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.

Define R to be a ring of characteristic not 2 or 3 satisfying the identity

(1)       (x,y,z) = (y,z,x)

for all x, y, z ∊ R, where by characteristic not p is meant x —> px is a one-toone mapping of R upon R. The associator (a, b, c) of R is defined by (a, b, c) = ab·c — a·bc. lf R also satisfies the identity

(2)      (x, x, x) = 0

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 130 - 141
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bruck, R. H. and Erwin Kleinfeld, The structure of alternative division rings, Proc. Amer. Math. Soc., 2 (1951), 878–890.Google Scholar
2. Kleinfeld, Erwin, Primitive alternative rings and semi-simplicity, Amer. J. Math., 77 (1955), 725–730.Google Scholar
3. Kleinfeld, Erwin, Alternative nil rings, Ann. of Math., 66 (1957), 395–399.Google Scholar
4. Kleinfeld, Erwin, Assosymmetric rings, Proc. Amer. Math. Soc., 8 (1957), 983–986.Google Scholar
5. Kleinfeld, Erwin, Associator dependent rings, Arch. Math., 13 (1962), 203–212.Google Scholar
6. Kleinfeld, Erwin, Frank Kosier, Osborn, J. M., and Rodabaugh, D., The structure of associator dependent rings, Trans. Amer. Math. Soc, 110 (1964), 473–483.Google Scholar
7. Zorn, Max, Alternativkörper und quadratische Système, Abh. Math. Sem. Hamb. Univ., 9 (1933), 395–402.Google Scholar