# Category:Units of Rings

Jump to navigation
Jump to search

This category contains results about **Units of Rings**.

Definitions specific to this category can be found in Definitions/Units of Rings.

Let $\struct {R, +, \circ}$ be a ring with unity whose unity is $1_R$.

### Definition 1

An element $x \in R$ is a **unit of $\struct {R, +, \circ}$** if and only if $x$ is invertible under $\circ$.

That is, a **unit** of $R$ is an element of $R$ which has an inverse.

- $\exists y \in R: x \circ y = 1_R = y \circ x$

### Definition 2

An element $x \in R$ is a **unit of $\struct {R, +, \circ}$** if and only if $x$ is divisor of $1_R$.

## Pages in category "Units of Rings"

The following 6 pages are in this category, out of 6 total.