Finitely generated may refer to:
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Finitely-generated module — In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R module also may be called a finite R module or finite over R.[1] Related concepts include finitely cogenerated modules, finitely… … Wikipedia
Finitely generated module — In mathematics, a finitely generated module is a module that has a finite generating set. Equivalently, it is a homomorphic image of a free module on finitely many generators. The kernel of this homomorphism need not be finitely generated (then… … Wikipedia
Finitely-generated abelian group — In abstract algebra, an abelian group (G,+) is called finitely generated if there exist finitely many elements x1,...,xs in G such that every x in G can be written in the form x = n1x1 + n2x2 + ... + nsxs with integers n1,...,ns. In this case, we … Wikipedia
Finitely generated abelian group — In abstract algebra, an abelian group ( G ,+) is called finitely generated if there exist finitely many elements x 1,..., x s in G such that every x in G can be written in the form : x = n 1 x 1 + n 2 x 2 + ... + n s x s with integers n 1,..., n… … Wikipedia
Finitely generated algebra — In mathematics, a finitely generated algebra is an associative algebra A over a field K such that every element of A can be expressed as a polynomial in a finite set of elements a 1, hellip;, a n of A , with coefficients in K . If it is necessary … Wikipedia
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 groups and roughly states that… … Wikipedia
Boundedly generated group — In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see harvnb|Lubotzky|Segal|2003) … Wikipedia
Compactly generated space — In topology, a compactly generated space (or k space) is a topological space whose topology is coherent with the family of all compact subspaces. Specifically, a topological space X is compactly generated if it satisfies the following condition:… … Wikipedia
Countably generated space — In mathematics, a topological space X is called countably generated if the topology of X is determined by the countable sets in a similar way as the topology of a sequential space (or a Fréchet space) by the convergent sequences. The countable… … Wikipedia
Stallings theorem about ends of groups — In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group G has more than one end if and only if the group G admits a nontrivial decomposition as an amalgamated free product or… … Wikipedia
