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Semiprime Rings with Nilpotent Derivatives

Published online by Cambridge University Press:  20 November 2018

L. O. Chung  and
Jiang Luh
L. O. Chung
Affiliation:
Department of Mathematics, N. C. State UniversityRaleigh, North Carolina 27650
Jiang Luh
Affiliation:
Department of Mathematics, N. C. State UniversityRaleigh, North Carolina 27650
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There has been a great deal of work recently concerning the relationship between the commutativity of a ring JR and the existence of certain specified derivations of R. Bell, Herstein, Procesei, Schacher, Ligh, Martindale, Putcha, Wilson, and Yaqub [1, 2, 6, 8, 9, 10, 11, 12, 14] have studied conditions on commutators which imply the commutativity of rings.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 415 - 421
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Bell, H., Duo rings, some applications to commutativity theorem, Canad. Math. Bull. 11 (1968), 375-380.Google Scholar
2. Bell, H., Some commutativity results for periodic rings, Acta Math. Sci. Hungarica. 28 (1976), 279-283.Google Scholar
3. Chung, L. O. and Luh, Jiang, Derivations of higher order and commutativity of rings (to appear).Google Scholar
4. Chung, L. O., Luh, Jiang and Richoux, A. N., Derivations and commutativity of rings, Pac. J. Mat. 80 (1979), 77-89.Google Scholar
5. Chung, L. O., Derivations and commutativity of rings II, Pac. J. Math. 85 (1979), 19-34 Google Scholar
6. Herstein, I. N., A condition for the commutativity of rings, Canad. J. Math. 9 (1957), 583-586.Google Scholar
7. Herstein, I. N., A note on derivations, Canad. Math. Bull. 21 (1978), 369-370.Google Scholar
8. Herstein, I. N., Center-like in prime rings, Notices of ams 26 No. 3 (1979) p. A-329.Google Scholar
9. Herstein, I. N., Procesi, C. and Schacher, M., Algebraic valued functions on non-commutative rings, J. of Algebr. 36 (1975), 128-150.Google Scholar
10. Ikeda, M. and Koc, C., On the commutator ideal of certain rings, Arch. Math. 25 (1974), 348-353.Google Scholar
11. Ligh, S., The structure of certain classes of rings and near rings, J. London Math. Soc. (2) 12 (1975), 27-31.Google Scholar
12. Martindale, W. S. III, The commutativity of a special class of rings, Canad. J. Math. 12 (1960), 263-268.Google Scholar
13. Posner, E. C., Derivations in prime rings, Proc. AM. 8 (1960), 1093-1100.Google Scholar
14. Putcha, M. S., Wilson, R. S. and Yaqub, A., Structure of rings satisfying certain identities on commutators, Proc. AM. 32 (1972), 57-62.Google Scholar