free abelian group
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English
Noun
free abelian group (plural free abelian groups)
- (algebra) a free module over the ring of integers
- A free abelian group of rank n is isomorphic to , where the ring of integers occurs n times as the summand. The rank of a free abelian group is the cardinality of its basis. The basis of a free abelian group is a subset of it such that any element of it can be expressed as a finite linear combination of elements of such basis, with the coefficients being integers. (For an element a of a free abelian group, 1a = a, 2a = a + a, 3a = a + a + a, etc., and 0a = 0, (−1)a = −a, (−2)a = −a + −a, (−3)a = −a + −a + −a, etc.)
