Definition:Generated Subring

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

Let $S \subseteq R$ be a subset.

The subring generated by $S$ is the smallest subring of $R$ containing $S$; that is, it is the intersection of all subrings of $R$ containing $S$.

Also see

 * Intersection of Subrings
 * Definition:Generator of Ring