Definition:Divisor (Algebra)/Factorization
< Definition:Divisor (Algebra)(Redirected from Definition:Factorization)
Jump to navigation
Jump to search
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