Definition:Generated Subring

Definition
Let $\struct {R, +, \circ}$ 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 is Subring
 * Definition:Generator of Ring
 * Definition:Generator of Algebra over Ring