代数结构
Sign in to saveAlso known as algebra, universal algebra
set equipped with one or more finitary operations defined on it
An algebraic structure is a set of objects paired with basic operations (like addition or multiplication) that you can perform on them. Algebraic structures matter because they provide a common framework for understanding how different mathematical systems work, making it easier to apply solutions from one area of math to another.
AI-generated from the Wikipedia summary — may contain errors.
Wikidata facts
- Subclass of
- structure
- Has part
- mathematical operation
Show 6 more facts
- underlying structure
- set
- maintained by WikiProject
- WikiProject Mathematics
- topic's main category
- Category:Algebraic structures
- topic has template
- Template:Algebraic structures
- studied by
- universal algebra
- Commons category
- Algebraic structures
Sources (3)
via Wikidata · CC0
Article · 中文
在泛代数中代数结构（英語：Algebraic structure）是在一种或多种运算下封闭的一个或多个集合。 例如，群、环、域、和格的代数结构。更复杂的结构可以被定义为通过引入多个操作，不同的基础集，或通过改变限定公理。更复杂的代数结构的实例包括向量空间，模和代數 (環論)。关于代数结构的的详细情况，参见各个链接。 一个代数结构包含集合及符合某些公理的运算或关系。 集U上定义二元运算形成的系统称为代数系统，如果对于任意a,b∈U,恒有（a·b)∈U。二元运算可推广至多元运算F,则相应的封闭性要求则改为：对于任意a,b,c,d,……∈U,恒有F(a,b,c,d,……)∈U。有的书上对封闭性未作要求，并称之为广群。运算f是一个从A×B→C的映射，若A=B=C,则称运算f是封闭的。
Abstract from DBpedia / Wikipedia · CC BY-SA