What does "abelian" mean?
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.
Abelian
/əˈbi.li.ən/ adj, noun
adj, noun ·Rare ·Advanced level
Meaning at a glance
- Primary sense: 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.
- Grammar: abelian is listed as adj, noun.
- Usage evidence: Every subgroup of an abelian group is abelian.
How to use "abelian"
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Meaning check
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Source and review context
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Before you rely on this definition
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Compare nearby meanings
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Definition decision workflow
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Final meaning check
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Definitions
Noun
- 1 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. historical
"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."
Adjective
- 1 Of an algebraic structure (usually a group or algebra), having a commutative defining operation. not-comparable
"The interesting aspect here is that U₃ is irreducible, even though all irreps over the complexes are one-dimensional because ℤ₄ is abelian."
- 2 Alternative letter-case form of abelian. alt-of, dated, not-comparable
"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."
- 3 Of a binary function, commutative. not-comparable
Example
"Every subgroup of an abelian group is abelian."
Common questions
How do you use "abelian" in a sentence?
Every subgroup of an abelian group is abelian.
How do you pronounce "abelian"?
Pronounced /əˈbi.li.ən/.
Etymology
Etymology 1
Name of the Norwegian mathematician Abel + -ian.
Etymology 2
From Abel + -ian.