# Naturally ordered groupoid

From Encyclopedia of Mathematics

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.

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#### References

[a1] | L. Fuchs, "Partially ordered algebraic systems" , Pergamon (1963) |

**How to Cite This Entry:**

Naturally ordered groupoid.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Naturally_ordered_groupoid&oldid=19093

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article