Definition:Unique Factorization Domain

Definition

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

If, for all $x \in D$ such that $x$ is non-zero and not a unit of $D$:

$(1): \quad x$ possesses a complete factorization in $D$

$(2): \quad$ Any two complete factorizations of $x$ in $D$ are equivalent

then $D$ is a unique factorization domain.

Sources

• Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 62$