Definition:Congruence Modulo an Ideal

Definition
Let $\struct {R, +, \circ}$ be a ring, and let $J$ be an ideal of $R$.

The notation:


 * $a \equiv b \pmod J$

is used to mean:


 * $a + \paren {-b} \in J$

Also known as
Sometimes the notation:


 * $\map a J b$

is used.