Definition:Congruence Modulo an Ideal

Definition

Let $\left({R, +, \circ}\right)$ be a ring, and let $J$ be an ideal of $R$.

The notation:

$a \equiv b \left({\bmod\, J}\right)$

is used to mean:

$a + \left({-b}\right) \in J$

Sometimes the notation:

$a \left({J}\right) b$

is used.