Definition of abelian in English:


Line breaks: abel|ian
Pronunciation: /əˈbiːlɪən


  • (Of a group) having members related by a commutative operation (i.e. a*b = b*a).
    More 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.

More definitions of abelian

Definition of abelian in:

Get more from Oxford Dictionaries

Subscribe to remove adverts and access premium resources

Word of the day coloratura
Pronunciation: ˌkɒlərəˈtjʊərə
elaborate ornamentation of a vocal melody