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
Factorization of a polynomial ring is also known as decomposition.
Linguistic Note
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.
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 62$. Factorization in an integral domain
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): factorization: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): factorization: 1.