Definition:Unital Subalgebra/Definition 1

Definition
Let $R$ be a commutative ring.

Let $\left({A_R, *}\right)$ be an unital algebra over $R$ whose unit is $1_A$.

Let $\left({B_R, *}\right)$ be a subalgebra of $A_R$.

The subalgebra $\left({B_R, *}\right)$ is a unital subalgebra of $A_R$ $1_A \in B$.

Also see

 * Equivalence of Definitions of Unital Subalgebra