Definition:Trivial Factorization

Definition
Let $\left({D, +, \circ}\right)$ be an integral domain.

Let $\left({U_D, \circ}\right)$ be the group of units of $\left({D, +, \circ}\right)$.

A factorization in $\left({D, +, \circ}\right)$ of the form $x = u \circ y$, where $u \in U_D$ (i.e. where $x$ is an associate of $y$) is called a trivial factorization.

A factorization in $\left({D, +, \circ}\right)$ of the form $x = z \circ y$, where neither $y$ nor $z$ is a unit of $D$, is called a non-trivial factorization.