free abelian group
Word Rarity
Very rare
Frequency: Zipf frequency 2.40 in modern English
24
Scrabble Score
16
Letters
3
Syllables
12
Unique Chars
Meaning
noun
A free module over the ring of integers.
Example Sentences
- "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.)"