# Category:Divisibility

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This category contains results about **Divisibility** in the context of **Abstract Algebra, in particular Ring Theory**.

Definitions specific to this category can be found in Definitions/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 $x \divides y$.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Divisibility"

The following 10 pages are in this category, out of 10 total.