Definition:Congruence Modulo an Ideal

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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.


Sources