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词条 Norm (abelian group)
释义

  1. Free abelian groups

  2. References

In mathematics, specifically abstract algebra, if (G, +) is an abelian group then is said to be a norm on the abelian group (G, +) if:

  1. ,
  2. ,
  3. .

The norm ν is discrete if there is some real number ρ > 0 such that ν(g) > ρ whenever g ≠ 0.

Free abelian groups

An abelian group is a free abelian group if and only if it has a discrete norm.[1]

References

1. ^{{citation | last = Steprāns | first = Juris | doi = 10.2307/2044776 | issue = 2 | journal = Proceedings of the American Mathematical Society | mr = 770551 | pages = 347–349 | title = A characterization of free abelian groups | volume = 93 | year = 1985}}
{{Abstract-algebra-stub}}

1 : Abelian group theory

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