Assertion: free abelian group | /r/HasProperty | free abelian
Facets:
value: conversely
type: DEGREE
value: in the category of abelian groups
type: OTHER
Source sentences:
text: A corollary to the fundamental theorem is that every finitely generated torsion-free abelian group is free abelian.
text: A finitely generated torsion-free abelian group is free.
text: The only free abelian groups that are free groups are the trivial group and the infinite cyclic group.
text: Free groups are the free objects in the category of groups, that is, the "most general" or "least constrained" groups with a given number of generators, whereas free abelian groups are the free objects in the category of abelian groups.
text: Conversely, all finitely generated torsion-free abelian groups are free abelian.