• (America) IPA: /əˈbi.li.ən/, /əˈbil.jən/

abelian (not comparable)

  1. (mathematics) Having a commutative defining operation. [Mid 19th century.]
Translations Related terms

abelian (not comparable)

  1. (mathematics, group theory, dated) Alternative letter-case form of abelian
    • 1904, Florian Cajori An Introduction to the Modern Theory of Equations, The MacMillan Company, page 214 ↗,
      Ex. 2. Show by §§ 187, 188 that there can be no transitive Abelian group of prime degree other than the cyclic group, and that there is no irreducible Abelian equation of prime degree other than the cyclic equation.
    • 1914, Charles Gustave Paul Kuschke, The Abelian Equations of the Tenth Degree Irreducible in a Given Domain of Rationality, University of California Press, page 118 ↗,
      All irreducible Abelian equations of the tenth order belong to the cyclical group of order ten, […] .
    • 2004, Friedrich Kasch, Adolf Mader, Rings, Modules, and the Total, Springer (Birkhäuser), page 101 ↗,
      In this chapter "group" means torsion free Abelian group. The "bible" of Abelian group theory is the two volume work of Fuchs [11].

abelian (plural abelians)

  1. (Roman Catholicism, historical) A member of a sect in fourth-century Africa mentioned by St. Augustine, who states that they married but lived in continence after the manner, as they claimed, of Abel.
    • 1826, unnamed translator, Pierre Bayle, An Historical and Critical Dictionary [1697, Dictionnaire Historique et Critique; 1709, Historical and Critical Dictionary], Selected and Abridged, Volume 1, page 50 ↗,
      The Abelians were only a moderate sort of Encratites and Novatians, who absolutely condemned matrimony, while the Abelians approved of and retained it.
    • 1833, James Flamank, A Treatise on Happiness, page 222 ↗,
      A difference of opinion existed as to the moral effects of matrimony among the early Christians; the Abelians, for instance, suffered no member of their sect to remain single, while the Novatians condemned marriage under every circumstance.
    • 1951, Reginald Reynolds, Beds: with many noteworthy instances of lying on, under, or about them, Doubleday, page 256 ↗,
      If we include heretical sects there is perhaps some similarity to be traced between the syneisaktism of certain Catholic enthusiasts and the customs of the Abelians or Abelonians, who took their name from Abel.
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