Zero and Unity of Subfield

Theorem

Let $\struct {F, +, \times}$ be a field whose zero is $0$ and whose unity is $1$.

Let $\struct {K, +, \times}$ be a subfield of $F$.

Zero of Subfield is Zero of Field

The zero of $\struct {K, +, \times}$ is also $0$.

Unity of Subfield is Unity of Field

The unity of $\struct {K, +, \times}$ is also $1$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): subfield
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): subfield