Definition of abelian in English: abelian
adjective Mathematics (of a group) having members related by a commutative operation (e.g., a×b = b×a)
Example sentences
‘Herbrand also worked on field theory considering abelian extensions of algebraic number fields.’ ‘After submitting a thesis on abelian functions, he received his doctorate in 1895 from the University of Strasbourg.’ ‘In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups.’ ‘Galois, after reading Abel and Jacobi's work, worked on the theory of elliptic functions and abelian integrals.’ ‘He does provide an example of the decomposition of an abelian group into cosets of a subgroup.’ ‘Schreier showed that the fundamental group of such a space is always abelian.’ ‘In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.’ Origin Mid 19th century: from N. H. Abel (see Abel, Niels Henrik) + -ian.