abelian en · ADJ
Pronunciation
- (Southern-England) audio
- (Southern-England) audio
- /əˈbil.jən/ (US)
- /əˈbiːlɪən/ (US)
- /əˈbi.li.ən/ (US)
- (Canada) audio
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.
Meanings
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(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:
- (not-comparable) Of a binary function, commutative.
Deriveds
abelianize · abelian group · semiabelian · anabelian · pre-abelian category · abelian algebra · abelianization · abelian ring · quasiabelian · nonabelian · abelian category · metabelian · abelian operation · abelianness
Relateds
Translations (37)
sv kommutativ (math: of an algebraic structure) · pt abeliano (math: of an algebraic structure) · fr abélien (math: of an algebraic structure) · it abeliano (math: of an algebraic structure) · sv abelsk (math: of an algebraic structure) · fr abélienne (math: of an algebraic structure) · fr commutatif (math: of an algebraic structure) · ru а́белев (math: of an algebraic structure) · es abeliano (math: of an algebraic structure) · nb abelsk (math: of an algebraic structure) · ca abelià (math: of an algebraic structure) · pl przemienna (math: of an algebraic structure) · et kommutatiivne (math: of an algebraic structure) · nb kommutativ (math: of an algebraic structure) · et Abeli (math: of an algebraic structure) · pl abelowa (math: of an algebraic structure) · de kommutativ (math: of an algebraic structure) · eu abeldar (math: of an algebraic structure) · fr commutative (math: of an algebraic structure) · fi Abelin (as in Abelin ryhmä) (math: of an algebraic structure) · ca commutatiu (math: of an algebraic structure) · cs Abelova (math: of an algebraic structure) · uk а́белів (math: of an algebraic structure) · hu abel (math: of an algebraic structure) · fi abelinen (math: of an algebraic structure) · cs komutativní (math: of an algebraic structure) · es conmutativo (math: of an algebraic structure) · da abelsk (math: of an algebraic structure) · de abelsch (math: of an algebraic structure) · eo abela (math: of an algebraic structure) · nl commutatief (math: of an algebraic structure) · nl abels (math: of an algebraic structure) · hy աբելյան (math: of an algebraic structure) · is abelskur (math: of an algebraic structure) · fi kommutatiivinen (math: of an algebraic structure) · cs abelovská (math: of an algebraic structure) · is Abel- (math: of an algebraic structure)