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abelian

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abelian¹

  • /əˈbi.li.ən/ US
  • /əˈbil.jən/ US
  • /əˈbiːlɪən/ US

Rhymes with -iən, -ɪljən, -iːliən

adjective

  1. not comparable Of an algebraic structure (usually a group or algebra), having a commutative defining operation. The interesting aspect here is that U₃ is irreducible, even though all irreps over the complexes are one-dimensional because ℤ₄ is abelian.
  2. not comparable Of a binary function, commutative.

Abelian²

adjective

  1. dated, not comparable Alternative letter-case form of abelian 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.

noun Abelians

  1. 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

    Similar: Abelite, Abelonian, Abelonite, Abeloite, Abenonite

Translations

Every language

adj math: of an algebraic structure

Españolabeliano, conmutativo
Portuguêsabeliano
Françaisabélien, abélienne, commutatif, commutative
Deutschabelsch, kommutativ
Italianoabeliano
Русскийа́белев ábelev

noun member of a sect living like Abel

Españolabelonita
Portuguêsabeliano
Françaisabélien, abélienne, abélite, abélonien, abélonienne
DeutschAbelianer, Abelianerin, Abelit, Abelitin

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MLA

"abelian." Wiktionary, via Micwyn, micwyn.com/word/abelian. Accessed 6 Nov. 2026.

APA

abelian. (n.d.). In Wiktionary, via Micwyn. Retrieved November 6, 2026, from https://micwyn.com/word/abelian

Chicago

"abelian." Wiktionary, via Micwyn. Accessed November 6, 2026. https://micwyn.com/word/abelian.

BibTeX
@misc{abelian_2026,
  title = {abelian},
  howpublished = {Wiktionary, via Micwyn},
  year = {2026},
  url = {https://micwyn.com/word/abelian},
  urldate = {2026-11-06}
}