finitely's Usage Examples:

generated (respectively finitely related, finitely presented) if it has a presentation that is finitely generated (respectively finitely related, a finite presentation).

abelian group ( G , + ) {\displaystyle (G,+)} is called finitely generated if there exist finitely many elements x 1 , … , x s {\displaystyle x_{1},\dots.

is the classification of finitely generated abelian groups which is a specialization of the structure theorem for finitely generated modules over a principal.

In mathematics, a finitely generated module is a module that has a finite generating set.

A finitely generated module over a ring R may also be called.

A finitely repeated game is a game in which the same one-shot stage game is played.

group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.

} Similarly, the Cartesian product of finitely many finite sets is finite.

{\displaystyle K(\{x_{1},\ldots ,x_{n}\}),} and one says that K(S) is finitely generated over K.

In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination.

If there is a finite set that generates M, then M is said to be a finitely generated monoid.

+ sign is used, all but finitely many coordinates must be zero, while if some form of multiplication is used, all but finitely many coordinates must be.

Look up finite, finitely, or finiteness in Wiktionary, the free dictionary.

R)\mid i\in I\}} such that for every x in P, fi(x) is only nonzero for finitely many i, and x = ∑ f i ( x ) a i {\displaystyle x=\sum f_{i}(x)a_{i}} .

The function μ {\displaystyle \mu } is called additive, or finitely additive, if, whenever A and B are disjoint sets in A {\displaystyle \scriptstyle.

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties.

can be axiomatized without schemata is said to be finitely axiomatized.

Theories that can be finitely axiomatized are seen as a bit more metamathematically.

infinite set), or which exhibit some pathological behavior (for example, finitely generated infinite torsion groups).

category is finitely complete if all finite limits exists (i.

Dually, a category is finitely cocomplete.

In other words, A contains all but finitely many elements of X.