Assertion: abelian group's element | /r/HasProperty | written
Facets:
value: uniquely
type: MANNER
Source sentences:
text: {\displaystyle \ e_{1}=(1,0)} and e 2 = ( 0 , 1 ) {\displaystyle \ e_{2}=(0,1)} , the element (4,3) can be written
text: there exists a subset of such that every element of can be written uniquely as , where is an integer and only finitely many s are nonzero 3 Freely generating set, in terms of universal property there exists a subset of the group such that any set map from that subset to any abelian group extends uniquely to a group homomorphism from the whole group to that abelian group there exists a subset of such that any set map from to an abelian group extends uniquely to a group homomorphism from to 4 Projective object in category of abelian groups any surjective homomorphism from an abelian group to it has a one-sided inverse for any surjective homomorphism with an abelian group, there exists an injective homomorphism such that is the identity map on .
text: In additive notation, the requirement for an element to be primitive is that each element of the group can be written as
text: An abelian group G is finitely generated if there are elements such that every element can be written as