Ring is Subring of Itself

Theorem

Let $R$ be a ring.

Then $R$ is a subring of itself.

Proof

$R$ is a ring and $R \subseteq R$.

It follows by definition that $R$ is a subring of $R$.

$\blacksquare$

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 56.1$ Subrings and subfields