Product order

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In mathematics, given two ordered sets A and B, one can induce a partial ordering on the Cartesian product A × B. Given two pairs (a1,b1) and (a2,b2) in A × B, one sets

(a1,b1) ≤ (a2,b2)

if and only if a1a2 and b1b2.

This ordering is called the product order. Another possible ordering on A × B is the lexicographical order.

The Cartesian product with product order is the categorical product in the category of partially ordered sets with monotone functions.


  • Neggers, J.; Kim, Hee Sik (1998), "4.2 Product Order and Lexicographic Order", Basic Posets, World Scientific, pp. 64–78, ISBN 9789810235895 .

See also[edit]