Definition:Complete Factorization

Definition
Let $\left({D, +, \circ}\right)$ 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 all of $y_1, y_2, \ldots, y_n$ are irreducible.

Linguistic Note
British English spells the word factorisation.