Associate elements

Definition

Two elements in a commutative unital ring are said to be associate elements if each one divides the other. The relation of being associate elements is an equivalence relation.

Facts

In an integral domain, two elements are associate if and only if they are in the same orbit under the multiplicative action of the group of units of the ring (or in other words, there is an invertible element that multiplied with the first gives the second). This is no longer true when the commutative unital ring has zero divisors.