General algebraic systems Free algebras Concept
Relatively free algebra
Summary
A relatively free algebra is an algebra that is free over some of its generating sets in the variety that it generates. The word "relatively" contrasts it with absolutely free algebras: it is free relative to the identities that it satisfies. Free groups, free abelian groups, free nilpotent groups of a given class and polynomial rings are relatively free. Relatively free algebras are exactly the free algebras of all varieties.
Further reading
About this page
| Tag | NYYV5V2FDD |
|---|---|
| URI | m2://NYYV5V2FDD |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08B20 |
| Specializes | Free algebra in a variety |
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