Category:Definitions/Divisors of Polynomials

This category contains definitions related to Divisors of Polynomials.
Related results can be found in Category:Divisors of Polynomials.

Let $D$ be an integral domain.

Let $D \sqbrk x$ be the polynomial ring in one variable over $D$.

Let $f, g \in D \sqbrk x$ be polynomials.

Then:

$f$ divides $g$

$f$ is a divisor of $g$

$g$ is divisible by $f$

if and only if:

$\exists h \in D \sqbrk x : g = f h$

This is denoted:

$f \divides g$