abelian

See also: Abelian

English

Etymology

Name of the Norwegian mathematician Abel +‎ -ian.

Pronunciation

• (US) IPA^(key): /əˈbi.li.ən/, /əˈbil.jən/, /əˈbiːlɪən/

• Audio (Southern England):

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• Audio (Southern England):

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• Audio (Canada):

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• Rhymes: -iən
• Rhymes: -ɪljən
• Rhymes: -iːliən

Adjective

abelian (not comparable)

1. (mathematics) Of an algebraic structure (usually a group or algebra), having a commutative defining operation. [Mid 19^th century.]
   • 1996, Barry Simon, Representations of Finite and Compact Groups, page 50:

     The interesting aspect here is that U₃ is irreducible, even though all irreps over the complexes are one-dimensional because ℤ₄ is abelian.

2. (mathematics) Of a binary function, commutative.

Derived terms

• abelian algebra
• abelian group
• abelianization
• abelianize
• abelianness
• abelian operation
• abelian ring
• anabelian
• metabelian
• nonabelian
• quasiabelian
• semiabelian

 

Translations

math: of an algebraic structure

• Armenian: աբելյան (abelyan)
• Basque: abeldar
• Catalan: abelià (ca), commutatiu (ca)
• Czech: Abelova f, abelovská f, komutativní
• Danish: abelsk
• Dutch: abels (nl), commutatief (nl)
• Esperanto: abela
• Estonian: Abeli (et), kommutatiivne
• Finnish: abelinen, kommutatiivinen (fi), Abelin (as in Abelin ryhmä)
• French: abélien (fr) m, abélienne (fr) f, commutatif (fr) m, commutative (fr) f
• German: abelsch, kommutativ (de)
• Icelandic: Abel- m, abelskur m
• Italian: abeliano (it)
• Norwegian:

  Bokmål: abelsk, kommutativ

• Polish: abelowa f, przemienna f
• Portuguese: abeliano
• Russian: а́белев (ru) (ábelev)
• Spanish: abeliano, conmutativo
• Swedish: abelsk (sv), kommutativ (sv)

See also

• Tauberian

Anagrams

• Liébana