Unital ring - Imported Knowlpedia Content

A unital ring is a ring $R$ together with an element $1\in R$ such that $1a=a1=a$ for all $a\in R$ .

Remarks

In a unital ring, elements that admit multiplicative inverses are units, and they form the group of units. Many constructions (e.g. polynomial rings) and many definitions of ring homomorphisms are most natural in the unital setting.

Examples

$\mathbb Z$ is unital with identity $1$ .
$M_n(R)$ is unital for any unital ring $R$ , with identity matrix $I_n$ .
$2\mathbb Z$ is a ring but not unital (its inherited multiplication has no identity element).