Definition:Unital Associative Commutative Algebra/Definition 1

Definition
Let $R$ be a commutative ring with unity.

A unitary algebra over $R$ is an algebra $\left({A, *}\right)$ over $R$ that has an identity element.

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

Also see

 * Equivalence of Definitions of Unitary Algebra