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
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