Field is Subfield of Itself

Theorem

Let $\struct {F, +, \circ}$ be a field.

Then $\struct {F, +, \circ}$ is a subfield of $\struct {F, +, \circ}$.

Proof

$F$ is a field and $F \subseteq F$ from Set is Subset of Itself.

$\blacksquare$

Sources

• 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 2$. Elementary Properties
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 56.1$ Subrings and subfields