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.
Comments
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
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