Definition:Generator of a Ring

Definition

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

Let $S \subseteq R$.

The subring generated by $S$ is the smallest subring of $R$ containing $S$.

Sources

• Seth Warner: Modern Algebra (1965): $\S 22$
• B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra (1970): $\S 2.3$: Definition $2.14$