General algebraic systems Congruences and quotients Concept
Quotient algebra
Summary
A quotient algebra is the algebra of classes of a congruence relation, with the operations computed on representatives. It generalizes the quotient group and the quotient ring. Every homomorphic image of an algebra is isomorphic to one of its quotients, by the homomorphism theorem.
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| Tag | N5KE7FH6CX |
|---|---|
| URI | m2://N5KE7FH6CX |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08A30 |
| Same as | |
| Changed | 2 November 2026 |
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Definitions
Used by
- Universal property of free algebras
- Variety as a reflective subcategory
- Reduced product
- Presentation of an algebra
- Birkhoff's subdirect representation theorem
- Correspondence theorem for congruences
- Homomorphism theorem
- Pseudovariety
- Associative quotient of a magma