Definition:Generator of Field

From ProofWiki
Jump to navigation Jump to search

Definition

Let $F$ be a field.

Let $S \subseteq F$ be a subset and $K \le F$ a subfield.


The field generated by $S$ is the smallest subfield of $F$ containing $S$.

The subring of $F$ generated by $K \cup S$, written $K \sqbrk S$, is the smallest subring of $F$ containing $K \cup S$.

The subfield of $F$ generated by $K \cup S$, written $\map K S$, is the smallest subfield of $F$ containing $K \cup S$.


Also see


Sources