Category:Congruence Relations

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This category contains results about 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:

$\forall x_1, x_2, y_1, y_2 \in S: \paren {x_1 \mathrel \RR x_2} \land \paren {y_1 \mathrel \RR y_2} \implies \paren {x_1 \circ y_1} \mathrel \RR \paren {x_2 \circ y_2}$

Subcategories

This category has the following 5 subcategories, out of 5 total.

Pages in category "Congruence Relations"

The following 24 pages are in this category, out of 24 total.