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.

Sources

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