Definition of abelian in English:

abelian

adjectiveəˈbiːlɪənəˈbēlyən

Mathematics

(of a group) having members related by a commutative operation (i.e. a*b = b*a).
〔数〕（群）交换的
Example sentencesExamples
- Herbrand also worked on field theory considering abelian extensions of algebraic number fields.
- Galois, after reading Abel and Jacobi's work, worked on the theory of elliptic functions and abelian integrals.
- In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.
- In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups.
- He does provide an example of the decomposition of an abelian group into cosets of a subgroup.
- After submitting a thesis on abelian functions, he received his doctorate in 1895 from the University of Strasbourg.
- Schreier showed that the fundamental group of such a space is always abelian.

Origin

Mid 19th century: from N. H. Abel (see Abel, Niels Henrik) + -ian.

Definition of abelian in US English:

abelian

adjectiveəˈbēlyən

Mathematics

(of a group) having members related by a commutative operation (e.g., a×b = b×a).
〔数〕（群）交换的
Example sentencesExamples
- After submitting a thesis on abelian functions, he received his doctorate in 1895 from the University of Strasbourg.
- He does provide an example of the decomposition of an abelian group into cosets of a subgroup.
- Schreier showed that the fundamental group of such a space is always abelian.
- Herbrand also worked on field theory considering abelian extensions of algebraic number fields.
- Galois, after reading Abel and Jacobi's work, worked on the theory of elliptic functions and abelian integrals.
- In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.
- In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups.

Origin

Mid 19th century: from N. H. Abel (see Abel, Niels Henrik) + -ian.

词汇	abelian
释义	Definition of abelian in English: abelian adjectiveəˈbiːlɪənəˈbēlyən Mathematics (of a group) having members related by a commutative operation (i.e. ab = ba). 〔数〕（群）交换的 Example sentencesExamples Herbrand also worked on field theory considering abelian extensions of algebraic number fields. Galois, after reading Abel and Jacobi's work, worked on the theory of elliptic functions and abelian integrals. In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators. In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups. He does provide an example of the decomposition of an abelian group into cosets of a subgroup. After submitting a thesis on abelian functions, he received his doctorate in 1895 from the University of Strasbourg. Schreier showed that the fundamental group of such a space is always abelian. Origin Mid 19th century: from N. H. Abel (see Abel, Niels Henrik) + -ian. Definition of abelian in US English: abelian adjectiveəˈbēlyən Mathematics (of a group) having members related by a commutative operation (e.g., a×b = b×a). 〔数〕（群）交换的 Example sentencesExamples After submitting a thesis on abelian functions, he received his doctorate in 1895 from the University of Strasbourg. He does provide an example of the decomposition of an abelian group into cosets of a subgroup. Schreier showed that the fundamental group of such a space is always abelian. Herbrand also worked on field theory considering abelian extensions of algebraic number fields. Galois, after reading Abel and Jacobi's work, worked on the theory of elliptic functions and abelian integrals. In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators. In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups. Origin Mid 19th century: from N. H. Abel (see Abel, Niels Henrik) + -ian.
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