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Line breaks: abel|ian
Pronunciation: /əˈbiːlɪən

Definition of abelian in English:


(Of a group) having members related by a commutative operation (i.e. a*b = b*a).
Example sentences
  • In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.
  • He does provide an example of the decomposition of an abelian group into cosets of a subgroup.
  • In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups.


mid 19th century: from N. H. Abel (see Abel, Niels Henrik) + -ian.

Definition of abelian in:

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