Category:Definitions/Congruence Relations
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This category contains definitions related to Congruence Relations.
Related results can be found in Category:Congruence Relations.
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:
- $\forall x_1, x_2, y_1, y_2 \in S: \paren {x_1 \mathrel \RR x_2} \land \paren {y_1 \mathrel \RR y_2} \implies \paren {x_1 \circ y_1} \mathrel \RR \paren {x_2 \circ y_2}$
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Pages in category "Definitions/Congruence Relations"
The following 2 pages are in this category, out of 2 total.