Definition:Trivial Factorization/Non-Trivial Factorization

Definition

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

Let $\struct {U_D, \circ}$ be the group of units of $\struct {D, +, \circ}$.

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

Linguistic Note

The spelling factorization is the US English version.

The UK English spelling is factorisation, but the tendency is for the literature to use the factorization form.

Sources

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