Definition:Subring

Let $$\left({R, +, \circ}\right)$$ be a ring.

A subring of $$\left({R, +, \circ}\right)$$ is a subset $$S$$ of $$R$$ such that $$\left({S, +_S, \circ_S}\right)$$ is also a ring.

See Subring Test.