Abelian

Pronunciation: /eɪˈbiːliən/

Definitions of abelian

adjective referring to a mathematical structure in which a certain operation is commutative

Example Sentences

A1 An abelian group is a mathematical concept.

A2 In mathematics, an abelian group is a group in which the group operation is commutative.

B1 The concept of abelian groups is essential in abstract algebra.

B2 Abelian groups play a crucial role in the study of group theory.

C1 Advanced algebraic structures such as abelian categories are studied in higher mathematics.

C2 The properties of abelian varieties are of interest to researchers in algebraic geometry.

Examples of abelian in a Sentence

formal The group is abelian if its group operation is commutative.

informal An abelian group is one where the order of operations doesn't matter.

slang Abelian groups are like the 'good boys' of group theory because they always follow the commutative rule.

figurative In a world of chaotic group operations, abelian groups stand out as the calm and orderly ones.

Grammatical Forms of abelian

• past tense: abelianized
• plural: abelians
• comparative: more abelian
• superlative: most abelian
• present tense: abelianizes
• future tense: will abelianize
• perfect tense: has abelianized
• continuous tense: is abelianizing
• singular: abelian
• positive degree: abelian
• infinitive: to abelianize
• gerund: abelianizing
• participle: abelianized

Origin and Evolution of abelian

First Known Use: 1870 year

Language of Origin: English

Story behind the word: The word 'abelian' originates from the name of the Norwegian mathematician Niels Henrik Abel, who made significant contributions to the field of mathematics.

Evolution of the word: Originally used in mathematics to describe a specific type of mathematical structure, the term 'abelian' has since evolved to be used more broadly in various fields to denote properties of objects that satisfy certain commutative properties.