Naturally ordered groupoid

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A partially ordered groupoid (cf. Partially ordered set; Groupoid) in which all elements are positive (that is, and for any ) and the larger of two elements is always divisible (on both the left and the right) by the smaller, that is, implies that for some . The positive cone of any partially ordered group (cf. Ordered group) is a naturally ordered semi-group.



[a1] L. Fuchs, "Partially ordered algebraic systems" , Pergamon (1963)
How to Cite This Entry:
Naturally ordered groupoid. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article