noun
Meaning 1
A free module over the ring of integers.
Definition source: English Wiktionary via Wiktextract
Topics: algebra, mathematics, sciences
Examples
- A free abelian group of rank n is isomorphic to Z⊕Z⊕...⊕Z=⨁nZ, where the ring of integers Z 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.)
Meaning relationships
Synonyms: none provided
Antonyms: none provided