abelian
/əˈbi.li.ən/
Word Rarity
Very rare
Frequency: 2.40 in modern English
9
Scrabble Score
7
Letters
1
Syllables
6
Unique Chars
Meaning
adj
Of an algebraic structure (usually a group or algebra), having a commutative defining operation.
adj
Of a binary function, commutative.
Example Sentences
- "The interesting aspect here is that U₃ is irreducible, even though all irreps over the complexes are one-dimensional because ℤ₄ is 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."
- "All irreducible Abelian equations of the tenth order belong to the cyclical group of order ten,[…]."
- "In this chapter "group" means torsion free Abelian group. The "bible" of Abelian group theory is the two volume work of Fuchs [11]."
- "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."
- "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."
Etymology
Etymology tree Norwegian Abel Proto-Indo-European *-(i)yós Proto-Italic *-ijos Proto-Italic *-ios Old Latin -ios Latin -ius Proto-Indo-European *-nós Proto-Italic *-nos Proto-Italic *-ānos Latin -ānus Latin -iānusbor. English -ian English abelian Name of the Norwegian mathematician Abel + -ian.
Word Breakdown
Regional Pronunciation
- American English: /əˈbi.li.ən/
Usage
Inflected Forms
Derived Forms
Phrases
abelian algebra
abelian category
abelian group
abelian operation
abelian ring
pre-abelian category
non-Abelian