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Sums of two regular elements

Published online by Cambridge University Press:  18 May 2009

J. C. Robson
J. C. Robson
Affiliation:
School of Mathematics, University of Leeds, Leeds, England, LS2 9JT
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A well-known fact concerning a prime right Goldie ring R, proved in [4, Section 5], is that an essential right ideal is generated by the regular elements which it contains. There is a modification of that proof which shows that each element of R is the sum of at most two regular elements. This suggested that the recent results of Chatters and Ginn [1] concerning rings generated by their regular elements might possibly be refined a little, since their arguments actually show that elements of R are sums of at most three regular elements.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 7 - 11
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Chatters, A. W. and Ginn, S. M., Rings generated by their regular elements, Glasgow Math. J. 25 (1984), 1–5.CrossRefGoogle Scholar
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3.Lambek, J., Lectures on rings and modules, 2nd ed. (Chelsea, 1976).Google Scholar
4.Robson, J. C., Artinian quotient rings, Proc. London Math. Soc. (3) 17 (1967), 600–616.CrossRefGoogle Scholar
5.Small, L. W. and Stafford, J. T., Regularity of zero divisors, Proc. London Math. Soc. (3) 44 (1982), 405–419.CrossRefGoogle Scholar