Definition:Quotient Ring

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

Let $$J$$ be an ideal of $$R$$.

Let addition be defined on $$\left({R / J, +, \circ}\right)$$ as here, and ring product be as defined here.

Let $$\equiv_J$$ be the congruence relation induced by $$J$$.

Then $$\left({R / J, +, \circ}\right)$$ is a ring called the quotient ring of $$R$$ and $$\equiv_J$$.

See Quotient Ring is a Ring.