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On the Ring of Quotients of a Boolean Ring

Published online by Cambridge University Press:  20 November 2018

B. Brainerd  and
J. Lambek
B. Brainerd
Affiliation:
The University of Western Ontario McGill University
J. Lambek
Affiliation:
The University of Western Ontario McGill University
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Two important mathematical constructions are: the construction of the rational s from the integers and the construction of the reals from the rationals. The first process can be carried out for any ring, producing its maximal ring of quotients [4, 5]. The second process can be carried out for any partially ordered set producing its Dedekind-MacNeille completion [2, p. 58]. We will show that for Boolean rings, which are both rings and partially ordered sets, the two constructions coincide.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 2 , Issue 1 , 01 January 1959 , pp. 25 - 29
Copyright
Copyright © Canadian Mathematical Society 1959

References

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3. Cartan, H. and Eilenberg, S., Homological algebra, (Princeton, 1956).Google Scholar
4. Findlay, G.D. and Lambek, J., A generalized ring of quotients, Can. Math. Bull. 1 (1958), 77-85, 155-167.Google Scholar
5. Utumi, Y., On quotient rings, Osaka Math. J. 8(1956), 1-18.Google Scholar