Category:Definitions/Divisibility

This category contains definitions related to Divisibility in the context of Abstract Algebra, in particular Ring Theory.
Related results can be found in Category:Divisibility.

Let $\struct {R, +, \circ}$ be an ring with unity whose zero is $0_R$ and whose unity is $1_R$.

Let $x, y \in D$.

We define the term $x$ divides $y$ in $R$ as follows:

$x \mathrel {\divides_R} y \iff \exists t \in R: y = t \circ x$

When no ambiguity results, the subscript is usually dropped, and $x$ divides $y$ in $R$ is just written $x \divides y$.