General algebraic systems Products and constructions Concept
Subdirect product
Summary
A subdirect product of a family of algebras is a subalgebra of their direct product that still projects onto each factor. It can be much smaller than the full product, yet it remembers each factor completely. By Birkhoff's subdirect representation theorem, every algebra is isomorphic to a subdirect product of subdirectly irreducible algebras.
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| Tag | 88WN3AD2VQ |
|---|---|
| URI | m2://88WN3AD2VQ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08B26 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Residually finite algebra
- Birkhoff's subdirect representation theorem
- Subdirectly irreducible algebra
- Boolean product