Assertion: abelian group | /r/HasProperty | free abelian
Facets:
value: by the above theorem
type: MANNER
Source sentences:
text: Theorem: An abelian group is free abelian if and only if it has a basis.
text: An Abelian group $F$ is free if and only if it has the projective property.
text: In mathematics, a free abelian group or free Z-module is an abelian group with a basis, or, equivalently, a free module over the integers.
text: An abelian group $K$ that is finitely generated has a finite basis and so by the above theorem is free abelian.