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
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $24$. The Division Algorithm