Editing Congruence relation (section)

=== Example: Rings ===
When an algebraic structure includes more than one operation, congruence relations are required to be compatible with each operation.  For example, a ring possesses both addition and multiplication, and a congruence relation on a ring must satisfy
: <math>r_1 + s_1 \equiv r_2 + s_2</math> and <math>r_1 s_1 \equiv r_2 s_2</math>
whenever <math>r_1 \equiv r_2</math> and <math>s_1 \equiv s_2</math>. For a congruence on a ring, the equivalence class containing 0 is always a two-sided [[ideal (ring theory)|ideal]], and the two operations on the set of equivalence classes define the corresponding quotient ring.