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Quotient Rings of a Class of Lattice-Ordered-Rings

Published online by Cambridge University Press:  20 November 2018

Stuart A. Steinberg
Stuart A. Steinberg*
Affiliation:
University of Toledo, Toledo, Ohio
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An f-ring R with zero right annihilator is called a qf-ring if its Utumi maximal left quotient ring Q = Q(R) can be made into and f-ring extension of R. F. W. Anderson [2, Theorem 3.1] has characterized unital qf-rings with the following conditions: For each q ∈ Q and for each pair d1, d2 ∈ R+ such that diq ∈ R

(i) (d1q)+ Λ (d2q)- = 0, and

(ii) d1 Λ d2 = 0 implies (d1q)+ Λ d2 = 0.

We remark that this characterization holds even when R does not have an identity element.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 627 - 645
Copyright
Copyright © Canadian Mathematical Society 1973

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