General algebraic systems Clones and operations Concept
Clone
Summary
A clone on a set is a set of finitary operations on that contains all projections and is closed under composition. The term operations of any algebra with universe form a clone, and every clone arises in this way. Clones let one compare algebras by what they can express, regardless of which basic operations were chosen. Two algebras on the same set with the same clone of term operations have the same subalgebras, congruences and automorphisms.
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About this page
| Tag | PTKR703G6A |
|---|---|
| URI | m2://PTKR703G6A |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08A40 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Algebraic approach to constraint satisfaction
- Sheffer function
- Lattice of clones
- Pol–Inv Galois connection
- Functional completeness
- Rosenberg's classification of maximal clones
- Minimal clone
- Post's lattice