Definition:Underlying Ring of Associative Algebra

Definition
Let $R$ be a commutative ring.

Let $(A, *)$ be an associative algebra over $R$.

Let $A = (M, +, \circ)$ be the underlying module of $(A, *)$.

The underlying ring of $(A, *)$ is the ring $(A, +, *)$.

Also see

 * Underlying Ring of Associative Algebra is Ring
 * Definition:Underlying Ringoid of Algebra