Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T00:37:16.299Z Has data issue: false hasContentIssue false
  • English
  • Français

A Classification of 2-Varieties

Published online by Cambridge University Press:  20 November 2018

Tim Anderson  and
Erwin Kleinfeld
Tim Anderson
Affiliation:
University of British Columbia, Vancouver, British Columbia
Erwin Kleinfeld
Affiliation:
University of British Columbia, Vancouver, British Columbia
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 purpose of this paper is to give a classification of those varieties of power-associative algebras over a field F which satisfy the condition

(1.1) For each A in and each ideal I of A, I2 is an ideal of A.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 348 - 364
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Albert, A. A., Almost alternative algebras, Port. Math. 8 (1949), 23–36.Google Scholar
2. Albert, A. A., Power-associative rings, Trans. Amer. Math. Soc. 64 (1948), 552–593.Google Scholar
3. Anderson, T., The Levitzki radical in varieties of algebras, Math. Ann. 194 (1971), 27–34.Google Scholar
4. Anderson, T., On the Levitzki radical, Can. Math. Bull. 17 (1974), 5–10.Google Scholar
5. Divinsky, N., Rings and radicals (University of Toronto Press, 1965).Google Scholar
6. Hentzel, I. R., Nil semi-simple (-1 , 1) rings, J. Algebra 22 (1972), 442–450.Google Scholar
7. Hentzel, I. R., (-1, 1) algebras, Proc. Amer. Math. Soc. 24 (1970), 24–28.Google Scholar
8. Hentzel, I. R., (-1, 1) rings, Proc. Amer. Math. Soc. 22 (1969), 367–374.Google Scholar
9. Kleinfeld, E., Simple rings of type (1,1) are associative, Can. J. Math. 13 (1961), 129–148.Google Scholar
10. Kleinfeld, E., Rings of (T, S) type, Port Math. 18 (1959), 107–110.Google Scholar
11. Kleinfeld, E., Associator dependent rings, Arch. Math. 13 (1962), 203–212.Google Scholar
12. Kleinfeld, E., Rosier, F., J. Osborne, M. and Rodabaugh, D., The structure of associator dependent rings, Trans. Amer. Math. Soc. 110 (1964), 473–483.Google Scholar
13. Kokoris, L., On rings of (T, h)-type, Proc. Amer. Math. Soc. 9 (1958), 897–904.Google Scholar
14. Maneri, C., Simple ( — 1, 1) rings with idempotent, Proc. Amer. Math. Soc. 14 (1963), 110–117.Google Scholar
15. Osborne, J. M., Varieties of algebras, Advances in Math. 8 (1972), 163–369.Google Scholar
16. Schafer, R. D., An introduction to nonas so dative algebras (Academic Press, New York, 1966).Google Scholar
17. Zwier, P., Prime ideals in a large class of nonas so dative rings, Trans. Amer. Math. Soc. 188 (1971), 257–271.Google Scholar