Definition:Generated Ring Extension

Definition
Let $S$ be a commutative rings with unity.

Let $R$ be a subring of $S$ with unity such that the unity of $R$ is the unity of $S$.

That is, $S$ is a ring extension of $R$.

Let $T \subseteq S$ be a subset of $S$.

Also see

 * Equivalence of Definitions of Generated Ring Extension
 * Definition:Generated Field Extension
 * Definition:Generated Subalgebra over Ring