Definition:Ring under Ring

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

A ring under $A$ is a pair $(B, f)$ where:
 * $B$ is a commutative ring with unity
 * $f : A \to B$ is a unital ring homomorphism

Also see

 * Definition:Unital Associative Commutative Algebra
 * Definition:Coslice Category