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On a Sheaf of Division Rings*

Published online by Cambridge University Press:  20 November 2018

George Szeto
George Szeto*
Affiliation:
Mathematics Department, Bradley University, Peoria, Illinois61606
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R. Arens and I. Kaplansky ([1]) call a ring A biregular if every two sided principal ideal of A is generated by a central idempotent and a ring A strongly regular if for any a in A there exists b in A such that a=a2b. In ([1], Sections 2 and 3), a lot of interesting properties of a biregular ring and a strongly regular ring are given. Some more properties can also be found in [3], [5], [8], [9] and [13]. For example, J. Dauns and K. Hofmann ([3]) show that a biregular ring A is isomorphic with the global sections of the sheaf of simple rings A/K where K are maximal ideals of A. The converse is also proved by R. Pierce ([9], Th. 11–1). Moreover, J. Lambek ([5], Th. 1) extends the above representation of a biregular ring to a symmetric module.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 727 - 731
Copyright
Copyright © Canadian Mathematical Society 1975

Footnotes

†

The author wishes to thank the referee for his valuable comments and suggestions.

*

This work was supported from the National Science Foundation Grant GU-3320.

References

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