Rugal

Group Definition

If we have element a and operator * that conform the following property.

group property

  1. 封闭性（Closure）
\[\text{if } a, b \in G \text{ then } a*b \in G\]
  1. 结合律（Associativity）
\[\text{if } a, b, c \in G \text{ then } (a*b)*c = a*(b*c)\]
  1. 同一/恒等/单位元 （Identity）
\[\exists e \Rightarrow \forall a, e * a = a * e = a\]
  1. 逆元（Inverse）
\[\text{if } a \in G, \exists a^{-1}, \text{then } a * a^{-1} = e\]

different group

  • C A ID IN  
    semigroup $\checkmark$ $\checkmark$    
    monoid $\checkmark$ $\checkmark$ $\checkmark$  
    group $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$

Published

31 January 2023

Category

development

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