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free abelian group. In DICTIOUS you will not only get to know all the dictionary meanings for the word
free abelian group, but we will also tell you about its etymology, its characteristics and you will know how to say
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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.)
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