Ivan Shishkin, Birch Grove

Unital magma

Concept history

A revision trail for this concept page.

3 revisions

Back

Revision 759

7/31/2026, 1:31:26 PM · Ancient Tree

Concept edited

Recorded titleUnital magma
Recorded typeDefinition
Compare with revision 74910 changed lines
1A magma $(M,*)$ is said unital if there exists an element $e\in M$, called neutral, such that for all $x\in M$:
1A [[Magma|magma]] $(M,*)$ is said unital if there exists an element $e\in M$, called [[Identity element|identity element]], such that for all $x\in M$:
2$$
3x*e=x=e*x
3x*e=x=e*x.
4$$
5By definition, the neutral has to be unique.
6
7Example:
6##### Remarks
7- The identity element is unique.
8
9##### Examples
8$\bullet$ If $(M,*)=(\Z,+)$, then $e=0$.
9$\bullet$ If $(M,* )=(\R^*,\cdot)$ then $e=1$.

Revision 749

7/31/2026, 9:54:49 AM · Sequoia

Concept edited

This older revision predates detailed metadata tracking.

Revision 748

7/31/2026, 9:54:28 AM · Sequoia

Concept created

A magma $(M,*)$ is said unital if there exists an element $e\in M$, called neutral, such that for all $x\in M$:
$$
x*e=x=e*x
$$
By definition, the neutral has to be unique. 

Example: 
$\bullet$ If $(M,*)=(\Z,+)$, then $e=0$.
$\bullet$ If $(M,* )=(\R^*,\cdot)$ then $e=1$.