Definition:Divisor (Algebra)/Terminology

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Definition

Let $\struct {R, +, \times}$ be a ring.

Let $x, y \in R$.


Let $x \divides y$ denote that $x$ divides $y$.

Then the following terminology can be used:

$x$ is a divisor of $y$
$y$ is a multiple of $x$
$y$ is divisible by $x$.


In the field of Euclidean geometry, in particular:

$x$ measures $y$.


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