Definition:Generated Division Subring

Definition

Let $\struct {D, +, \circ}$ be a division ring.

Let $S \subseteq D$.

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

Also see

• Definition:Generator of Division Ring

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $23$. The Field of Rational Numbers