abelian
US/əˈbi.li.ən/
abelian adjective: of an algebraic structure (usually a group or algebra), having a commutative defining operation.
Adjective (1)
abelian (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.1996, Barry Simon, Representations of Finite and Compact Groups, page 50
- Of a binary function, commutative.
Adjective (2) capitalized: Abelian
Abelian (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.1904, Florian Cajori, An Introduction to the Modern Theory of Equations, The MacMillan Company, page 214
- All irreducible Abelian equations of the tenth order belong to the cyclical group of order ten,[…].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
Noun capitalized: Abelian
Abelian (plural Abelians)
- 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.
- The Abelians were only a moderate sort of Encratites and Novatians, who absolutely condemned matrimony, while the Abelians approved of and retained it.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...
- 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.1833, James Flamank, A Treatise on Happiness, page 222
Synonyms of abelian
Forms of abelian
| plural | Abelians |
|---|
Origin of abelian
Name of the Norwegian mathematician Abel + -ian.
From Abel + -ian.
Words formed from abelian
- non-Abelian
- abelian algebra
- abelian category
- abelian group
- abelianization
- abelianize
- abelianness
- abelian operation
- abelian ring
- anabelian
- metabelian
- nonabelian
- pre-abelian category
- quasiabelian
- semiabelian
Phrases with abelian
Words that rhyme with abelian
Questions about abelian
- What does abelian mean?
- Abelian means of an algebraic structure (usually a group or algebra), having a commutative defining operation.
- What part of speech is abelian?
- Abelian can be an adjective or a noun.
- How do you pronounce abelian?
- Abelian is pronounced /əˈbi.li.ən/ (US).
Words near abelian in the dictionary
Source and license
Adapted from Wiktionary: abelian (page history and authors); Abelian (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Cite this entry: “abelian.” Word.ws, https://word.ws/abelian. Based on Wiktionary, CC BY-SA 4.0.