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Lattice-Ordered Rings of Quotients

Published online by Cambridge University Press:  20 November 2018

F. W. Anderson
F. W. Anderson*
Affiliation:
Institute for Advanced Study and University of Oregon
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R. E. Johnson (10), Utumi (18), and Findlayand Lambek (7) have defined for each ring R a unique maximal "ring of right quotients" Q. When R is a commutative integral domain (in this paper an integral domain need not be commutative) or an Ore domain, then Q is the usual division ring of quotients of R. Moreover, it is well known that in these special cases, if R is totally ordered, then so is Q.

The main purpose of this paper is to study the ring of quotients Q, and in particular its order properties, for certain lattice-ordered rings R.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 434 - 448
Copyright
Copyright © Canadian Mathematical Society 1965

References

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