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A Note on a Fully Ordered Ring

Published online by Cambridge University Press:  20 November 2018

Kwangil Koh*
Affiliation:
North Carolina State University, Raleigh
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A ring R (associative ring) is said to be fully ordered provided that R is a linearly ordered set under a relation such that for any a, b and c in R, implies that and if c ε 0 then and . We say a subset K of R is convex provided that if a, b ε K such that then the interval [a, b] is a subset of K. Obviously an additive subgroup K of R is convex if and only if b ε K and b > 0 implies [a, b] ⊆ K.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Fuchs, L., Partially Ordered Algebraic Systems, Pergammon Press (1966).Google Scholar