Definition:Divisor (Algebra)/Factorization

Definition

Let $x, y \in D$ where $\struct {D, +, \times}$ is an integral domain.

Let $x$ be a divisor of $y$.

Then by definition it is possible to find some $t \in D$ such that $y = t \times x$.

The act of breaking down such a $y$ into the product $t \circ x$ is called factorization.

Also known as

When $D$ is a polynomial ring, the term decomposition can sometimes be found for 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