# nLab unital magma

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Definition

A magma $(S,\cdot)$ is called unital if it has an identity element $1 \in S$, hence an element such that for all $x \in S$ it satisfies the equation

$1 \cdot x = x = x \cdot 1$

holds. The identity element is idempotent.

Some authors take a magma to be unital by default (cf. Borceux-Bourn Def. 1.2.1).

## Examples

Examples include unital rings etc.

Last revised on January 26, 2020 at 02:00:39. See the history of this page for a list of all contributions to it.