Definition:Divisor (Algebra)/Factorization

Definition
Let $x, y \in D$ where $\left({D, +, \times}\right)$ 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 UK English spelling is factorisation.