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.

Factorization of a polynomial ring is also known as decomposition.

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.