Category:Definitions/Unital Algebras

This category contains definitions related to Unital Algebras.
Related results can be found in Category:Unital Algebras.

Let $R$ be a commutative ring.

Let $\struct {A, *}$ be an algebra over $R$.

Then $\struct {A, *}$ is a unital algebra if and only if the algebraic structure $\struct {A, \oplus}$ has an identity element.

That is:

$\exists 1_A \in A: \forall a \in A: a * 1_A = 1_A * a = a$