Phrase
algebraic structure
noun
代数结构
A mathematical object made up of a carrier set (underlying set), an optional scalar set, a set of operations (usually binary), and a set of axioms.
- 1.
A mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.
由载体集合(也称底层集合或域)、可选标量集合、一组运算(通常为二元运算,但也可为有限元运算)以及这些运算必须满足的一组恒等式(公理)组成的数学对象
由载体集合(也称底层集合或域)、可选标量集合、一组运算(通常为二元运算,但也可为有限元运算)以及这些运算必须满足的一组恒等式(公理)组成的数学对象
In use
An algebraic structure is a set equipped with one or more operations.
We study group theory because it is a fundamental algebraic structure.
In mathematics, an algebraic structure consists of a set and operations.
[noun] is an algebraic structure
A group is an algebraic structure.
群是一种代数结构。
study [algebraic structures]
In abstract algebra, we study various algebraic structures.
在抽象代数中，我们研究各种代数结构。
define [an algebraic structure] on [set]
Connections
Confusing words
- algebraic system
- 代数系统 · “代数结构”强调集合与运算的整体框架，而“代数系统”通常指具体的实例，如一个群或环。
- algebraic model
- 代数模型 · “代数模型”指满足特定公理的数学结构，常用于逻辑或模型论；而“代数结构”是更广义的术语，涵盖所有此类对象。
Word family
- algebra
- 代数 · n.
- structural
- 结构的 · adj.
- structurally
- 结构上 · adv.
- structured
- 有结构的 · adj.
Learner notes
Learn the forms together
页面下方列出了常见词形变化。学习时注意它们在句子中的语法位置。
Dictionary facts from WIKTIONARY.