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