Editing Divisor (section)

== In abstract algebra ==
=== Ring theory ===
{{Main|Divisibility (ring theory)}}

=== Division lattice ===
{{Main|Division lattice}}
In definitions that allow the divisor to be 0, the relation of divisibility turns the set <math>\mathbb{N}</math> of [[non-negative]] integers into a [[partially ordered set]] that is a [[lattice (order)|complete distributive lattice]]. The largest element of this lattice is 0 and the smallest is 1. The meet operation '''∧''' is given by the [[greatest common divisor]] and the join operation '''∨''' by the [[least common multiple]]. This lattice is isomorphic to the [[duality (order theory)|dual]] of the [[lattice of subgroups]] of the infinite [[cyclic group]] Z.