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Annihilators in semiprime right Goldie rings

Published online by Cambridge University Press:  20 January 2009

C. R. Hajarnavis
C. R. Hajarnavis
Affiliation:
Mathematics InstituteUniversity of WarwickCoventry CV4 7AL, United Kingdom
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(i) Let R be a semiprime right Goldie ring with dim R = n. Then a maximal chain of right annihilators in R has exactly n terms, (ii) A semiprime locally right Goldie ring with ACC and DCC on right annihilators is a right Goldie ring.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 1 , February 1992 , pp. 133 - 137
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Brown, K. A. and Wehrfritz, B. A. F., Goldie criteria for some semiprime rings, J. Glasgow Math. Soc., to appear.Google Scholar
2.Chatters, A. W. and Hajarnavis, C. R., Rings with chain conditions (Research notes in mathematics, Pitman 1980).Google Scholar
3.Goldie, A. W., Rings with maximum condition (Lectures given at Yale University, Yale, 1961).Google Scholar
4.Goldie, A. W., Semi-prime rings with maximum condition, Proc. London Math. Soc. (3) 10 (1960), 201–220.CrossRefGoogle Scholar
5.Herstein, I. and Small, L. W., Nil rings satisfying certain chain conditions, Canad. J. Math. 16 (1964), 771–776.CrossRefGoogle Scholar
6.Johnson, R. E. and Levy, L. S., Regular elements in semiprime rings, Proc. Amer. Math. Soc. 19 (1968), 961–963.CrossRefGoogle Scholar