French translation of
abelian
is
abélien
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Meaning of "abelian" in English
In mathematics, "abelian" refers to a type of group that is commutative, meaning the group operation's result does not depend on the order of the elements. Named after the mathematician Niels Henrik Abel, abelian groups play a fundamental role in abstract algebra. They are characterized by the condition that for any two elements in the group, the operation between them results in the same outcome regardless of their order. Abelian groups are important due to their structured yet simple properties, making them easier to study and apply in various mathematical contexts.
Meaning of "abélien" in French
The term "abélien," similar to its English counterpart, refers to a commutative group in mathematics. It signifies a mathematical structure where the order of elements in an operation does not affect the result. Named after Norwegian mathematician Niels Henrik Abel, abélien groups are central to the study of algebra as they form a class of structures that can be thoroughly analyzed and utilized in diverse mathematical fields. The concept remains largely the same across languages, highlighting the universality of mathematical ideas.
Pronunciation of "abelian" in English
Phonetic Transcription: /əˈbiː.li.ən/
Pronunciation Variations: Depending on regional accents, such as British or American English, there might be slight differences in the vowel sounds, particularly in the first syllable.
Pronunciation of "abélien" in French
Phonetic Transcription: /a.be.ljɛ̃/
Pronunciation Variations: Regional accents in French may affect the nasal sound and the stress on the syllables slightly, but the pronunciation is largely consistent across French-speaking regions.
Sentence examples in English and translation to French
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The structure of an Abelian group simplifies many problems in algebra.
(La structure d'un groupe abélien simplifie de nombreux problèmes en algèbre.) -
Abelian groups are commutative, making calculations straightforward.
(Les groupes abéliens sont commutatifs, ce qui rend les calculs simples.) -
Studying Abelian groups is fundamental in mathematical research.
(Étudier les groupes abéliens est fondamental dans la recherche mathématique.) -
The properties of Abelian rings are similar to those of Abelian groups.
(Les propriétés des anneaux abéliens sont similaires à celles des groupes abéliens.) -
Understanding Abelian structures helps in solving complex equations.
(Comprendre les structures abéliennes aide à résoudre des équations complexes.) -
Abelian categories provide a framework for homological algebra.
(Les catégories abéliennes fournissent un cadre pour l'algèbre homologique.) -
The set of integers with addition forms an Abelian group.
(L'ensemble des entiers avec addition forme un groupe abélien.) -
Many mathematical branches rely on the concept of Abelian groups.
(De nombreuses branches mathématiques reposent sur le concept de groupes abéliens.) -
Abelian varieties are significant in the field of algebraic geometry.
(Les variétés abéliennes sont importantes dans le domaine de la géométrie algébrique.) -
Researchers often explore the limits of Abelian group theory.
(Les chercheurs explorent souvent les limites de la théorie des groupes abéliens.)
Synonyms, antonyms, and similar words for "abelian" in English
Synonyms: commutative, interchangeable
Antonyms: noncommutative
Similar Words: group, algebraic, mathematical, symmetric, associative
Synonyms, antonyms, and similar words for "abélien" in French
Synonyms: commutatif, interchangeable
Antonyms: non commutatif
Similar Words: groupe, algébrique, mathématique, symétrique, associatif
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