For faster navigation, this Iframe is preloading the Wikiwand page for 代数结构.

代数结构

维基百科,自由的百科全书

泛代数代数结构(英语:Algebraic structure)是在一种或多种运算下封闭的一个或多个集合[1]

例如,、和的代数结构。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代数 (环论)。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运算关系

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。

样例

单个集合的例子

简单结构: 没有定义二元运算的情况:

  • 集合: 没有定义二元运算的集合S可看成是一个退化的代数结构。

参阅

参考文献

  1. ^ P.M. Cohn. (1981) Universal Algebra, Springer, p. 41.

外部链接

{{bottomLinkPreText}} {{bottomLinkText}}
代数结构
Listen to this article

This browser is not supported by Wikiwand :(
Wikiwand requires a browser with modern capabilities in order to provide you with the best reading experience.
Please download and use one of the following browsers:

This article was just edited, click to reload
This article has been deleted on Wikipedia (Why?)

Back to homepage

Please click Add in the dialog above
Please click Allow in the top-left corner,
then click Install Now in the dialog
Please click Open in the download dialog,
then click Install
Please click the "Downloads" icon in the Safari toolbar, open the first download in the list,
then click Install
{{::$root.activation.text}}

Install Wikiwand

Install on Chrome Install on Firefox
Don't forget to rate us

Tell your friends about Wikiwand!

Gmail Facebook Twitter Link

Enjoying Wikiwand?

Tell your friends and spread the love:
Share on Gmail Share on Facebook Share on Twitter Share on Buffer

Our magic isn't perfect

You can help our automatic cover photo selection by reporting an unsuitable photo.

This photo is visually disturbing This photo is not a good choice

Thank you for helping!


Your input will affect cover photo selection, along with input from other users.