Definition:Unital Associative Commutative Algebra/Definition 1

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

A unital associative commutative algebra over $R$ is an algebra $\left({A, *}\right)$ over $R$ that is unital, associative and commutative and whose underlying module is unitary.

Also see

 * Equivalence of Definitions of Unital Associative Commutative Algebra