Category:Definitions/Quotient Epimorphisms
Jump to navigation
Jump to search
This category contains definitions related to Quotient Epimorphisms.
Related results can be found in Category:Quotient Epimorphisms.
Let $\RR$ be a congruence relation on an algebraic structure $\struct {S, \circ}$.
Let $q_\RR: \struct {S, \circ} \to \struct {S / \RR, \circ_\RR}$ denote the quotient mapping from $\struct {S, \circ}$ to the quotient structure $\struct {S / \RR, \circ_\RR}$:
- $\forall x \in S: \map {q_\RR} x = \eqclass x \RR$
where $\eqclass x \RR$ denotes the equivalence class of $x$ under $\RR$.
Then $q_\RR$ is referred to as the quotient epimorphism from $\struct {S, \circ}$ to $\struct {S / \RR, \circ_\RR}$.
Pages in category "Definitions/Quotient Epimorphisms"
The following 7 pages are in this category, out of 7 total.