In mathematics, **finitely generated** may refer to:

- Finitely generated group
- Finitely generated monoid
- Finitely generated abelian group
- Finitely generated module
- Finitely generated ideal
- Finitely generated algebra
- Finitely generated space

### Other articles related to "finitely generated, finitely, generated":

Structure Theorem For

... In mathematics, in the field of abstract algebra, the structure theorem for

**Finitely Generated**Modules Over A Principal Ideal Domain... In mathematics, in the field of abstract algebra, the structure theorem for

**finitely generated**modules over a principal ideal domain is a generalization of the fundamental theorem of**finitely generated**abelian ...Small Cancellation Theory - Applications

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**Finitely**presented C'(1/6) small cancellation groups are basic examples of word-hyperbolic groups ...**Finitely**presented groups given by finite C(4)–T(4) presentations where every piece has length one are basic examples of CAT(0) groups for such a presentation the universal cover ... with a proof that every countable group can be embedded into a simple group**generated**by an element of order two and an element of order three ...Stallings Theorem About Ends Of Groups - Ends of Groups - Cuts and Almost Invariant Sets - Cuts and Splittings Over Finite Groups

... If G = H∗K where H and K are nontrivial

... If G = H∗K where H and K are nontrivial

**finitely generated**groups then the Cayley graph of G has at least one essential cut and hence e(G) > 1 ... A more precise version of this argument shows that for a**finitely generated**group G If G = H∗CK is a free product with amalgamation where C is a finite group ... If is an HNN-extension where C1, C2 are isomorphic finite subgroups of H then G is a**finitely generated**group and e(G) > 1 ...Finitely-generated Algebra

... In mathematics, a

... In mathematics, a

**finitely generated**algebra is an associative algebra A over a field K where there exists a finite set of elements a1,…,an of A such that every ... emphasize the field K then the algebra is said to be**finitely generated**over K ... Algebras that are not**finitely generated**are called infinitely**generated**...### Famous quotes containing the word generated:

“It is precisely the purpose of the public opinion *generated* by the press to make the public incapable of judging, to insinuate into it the attitude of someone irresponsible, uninformed.”

—Walter Benjamin (1892–1940)

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