# Definition:Divisor (Algebra)/Factorization

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## 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