# Finitely Generated

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 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
... 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 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 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)