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词条„abelian group“在英语 » 德语中的译文 (跳至 德语 » 英语)

abelian group 名词

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As a set it is a singleton, and also has a trivial structure of abelian group.
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The term "non-abelian" is used to distinguish from the idea of an abelian group, where all of the elements of the group commute.
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The center is a characteristic subgroup and is also an abelian group (because, in particular, all elements of the center must commute with each other).
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Consider the abelian group (that is, the set with addition modulo 4), and its subgroup.
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This is achieved by putting an alternative abelian group structure on the normal invariants as described here.
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The number of independent generators is the rank of an abelian group.
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As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division satisfying the appropriate abelian group equations and distributive law.
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Somewhat akin to the dimension of vector spaces, every abelian group has a "rank".
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The same applies to flatness, since an abelian group is torsion-free if and only if it is flat.
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This is an abelian group for all "k".
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