Definition:Divisor (Algebra)/Factorization

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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.