Category:Quotient Structures

From ProofWiki
Jump to navigation Jump to search

This category contains results about Quotient Structures.

Let $\left({S, \circ}\right)$ be an algebraic structure.

Let $\mathcal R$ be a congruence relation on $\left({S, \circ}\right)$.

Let $S / \mathcal R$ be the quotient set of $S$ by $\mathcal R$.

Let $\circ_\mathcal R$ be the operation induced on $S / \mathcal R$ by $\circ$.

The quotient structure defined by $\mathcal R$ is the algebraic structure:

$\left({S / \mathcal R, \circ_\mathcal R}\right)$