Category:Examples of Congruence Relations
Jump to navigation
Jump to search
This category contains examples of Congruence Relation.
Let $\struct {S, \circ}$ be an algebraic structure.
Let $\RR$ be an equivalence relation on $S$.
Then $\RR$ is a congruence relation for $\circ$ if and only if:
- $\forall x_1, x_2, y_1, y_2 \in S: \paren {x_1 \mathrel \RR x_2} \land \paren {y_1 \mathrel \RR y_2} \implies \paren {x_1 \circ y_1} \mathrel \RR \paren {x_2 \circ y_2}$
Pages in category "Examples of Congruence Relations"
The following 17 pages are in this category, out of 17 total.
A
C
- Congruence Modulo Normal Subgroup is Congruence Relation
- Congruence Relation/Examples
- Congruence Relation/Examples/Equal Fourth Powers over Complex Numbers for Addition
- Congruence Relation/Examples/Equal Fourth Powers over Complex Numbers for Multiplication
- Congruence Relation/Examples/Equal Sine of pi x over 6 on Integers for Addition
- Congruence Relation/Examples/Equal Sine of pi x over 6 on Integers for Multiplication