Definition:Complete Factorization

Definition
Let $\struct {D, +, \circ}$ be an integral domain.

Let $x$ be a non-zero non-unit element of $D$.

A complete factorization of $x$ in $D$ is a tidy factorization:


 * $x = u \circ y_1 \circ y_2 \circ \cdots \circ y_n$

such that:
 * $u$ is a unit of $D$
 * all of $y_1, y_2, \ldots, y_n$ are irreducible in $D$.