Topic summary

Prime field

Extracted from the Wikipedia article Field (mathematics).

Subfields and prime fields

A subfield $E$ of a field $F$ is a subset of $F$ that is a field with respect to the field operations of $F$ . Equivalently $E$ is a subset of $F$ that contains $1$ , and is closed under addition, multiplication, additive inverse and multiplicative inverse of a nonzero element. This means that $1 ∊ E$ , that for all $a, b ∊ E$ both $a + b$ and $a \cdot b$ are in $E$ , and that for all $a \neq 0$ in $E$ , both $- a$ and $1/ a$ are in $E$ .

Wikipedia source