General algebraic systems Homomorphisms and substructures Concept
Finitely generated algebra
Summary
An algebra is finitely generated when some finite subset of it generates the whole algebra. Every element can then be built from finitely many fixed elements by repeated use of the operations. Finitely generated groups, rings and lattices are all special cases. In the subalgebra lattice, the finitely generated subalgebras are exactly the compact elements.
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| Tag | WR4WF1K2KW |
|---|---|
| URI | m2://WR4WF1K2KW |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08A30, 08A05 |
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