Definition:Divisor (Algebra)/Integer

Definition
Let $\left({\Z, +, \times}\right)$ be the ring of integers.

Let $x, y \in \Z$.

Then $x$ divides $y$ is defined as:
 * $x \mathrel \backslash y \iff \exists t \in \Z: y = t \times x$

Notation
If $x \mathrel \backslash y$, then:
 * $x$ is a divisor of $y$
 * $y$ is a multiple of $x$
 * $y$ is divisible by $x$.

To indicate that $x$ does not divide $y$, we write $x \nmid y$.

Also known as
A divisor is also known as a factor.

Generalizations

 * Definition:Divisor in Integral Domain
 * Definition:Divisor of Ring Element