Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-09-12T10:21:21.845Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Banaschewski, B., Hüllensysteme and Erweiterung von Quasiordnungen, Zeitschr. f. math. Logik and Grundlag?n d. Math. 2(1956), 117-130.Google Scholar
2. Birkhoff, G., Lattice theory, (New York, 1948).Google Scholar
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