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A Counterexample to a Conjecture of D.F. Sanderson

Published online by Cambridge University Press:  20 November 2018

Israel Kleiner
Israel Kleiner*
Affiliation:
York University, Toronto
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In [2, p. 511] Sanderson has shown that if every Large left ideal of a ring R with identity contains a regular element, and if the regular elements in R satisfy Ore's condition, then the complete (Utumi's) ring of quotients coincides with the classical ring of quotients. He conjectured that the above conditions are also necessary. The following is a counter example.

Type
Notes and Problems
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 4 , October 1966 , pp. 517
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Lambek, J., Lectures on rings and modules. Blaisdell, New York, (1966).Google Scholar
2. Sanderson, D.F., A generalization of divisibility and injectivity in modules, Can. Math. Bull. 8, (1965), 505-513.Google Scholar