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Generalized Commutative Rings

Published online by Cambridge University Press:  22 January 2016

L. P. Belluce ,
I. N. Herstein  and
S. K. Jain
L. P. Belluce
Affiliation:
University of California, Riversides
I. N. Herstein
Affiliation:
University of Chicago
S. K. Jain
Affiliation:
University of California, Riversides
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Among his various interests in algebra Nakayama also took part in the various researches, published in the early and middle 1950’s, which dealt with the commutativity of rings. This paper, which studies a problem of a related sort, thus seems appropriate in a Journal honoring his memory.

We shall study a certain class of rings which satisfy a weak form of the commutative law and shall show that the structure of such rings can be determined.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 1 - 5
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Faith, C., Algebraic division ring extensions, Proc. A. M.S. vol. 11 (1960), pp. 43–53.Google Scholar
[2] Faith, C., Radical extensions of rings, Proc. A.M.S. vol. 12 (1961), pp. 274–283.CrossRefGoogle Scholar
[3] Herstein, I. N., Two remarks on the commutativity of rings, Canadian J. Math. vol. 5 (1953), pp. 242–244.Google Scholar
[4] Nakayama, T., Über die Kommutativität gewisser Ringe, Abh. Math. Seminar Hamburg, vol. 20 (1955), pp. 20–27.Google Scholar
[5] Nakayama, T., A remark on the commutativity of algebraic rings, Nagoya Math. Jour. vol. 14 (1959), pp. 39–44.CrossRefGoogle Scholar