abelian

abelian

See also: Abelian

English

Etymology

Name of the Norwegian mathematician Abel +‎ -ian.

Pronunciation

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

• Audio (UK)

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• Audio (UK)

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• Audio (CA)

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Adjective

abelian (not comparable)

1. (mathematics) Of an algebraic structure, having a commutative defining operation. [Mid 19^th century.][1]
   • 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.

Related terms

• abelian algebra
• abelian group
• abelian operation
• abelian ring

Translations

math: of a group

Catalan: abelià (ca), commutatiu 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

References

1. Lesley Brown, editor-in-chief; William R. Trumble and Angus Stevenson, editors (2002), “abelian”, in The Shorter Oxford English Dictionary on Historical Principles, 5th edition, Oxford; New York, N.Y.: Oxford University Press, →ISBN, page 3.

Anagrams

• Liébana