Commutative inverse semigroups
Abbreviation: CInvSgrp
Definition
A commutative inverse semigroup is an inverse semigroups $\mathbf{S}=\langle S,\cdot,^{-1}\rangle $ such that
$\cdot$ is commutative: $xy=yx$
Definition
A commutative inverse semigroup is a structure $\mathbf{S}=\langle S,\cdot,^{-1}\rangle $ such that
$\cdot$ is associative: $(xy)z=x(yz)$
$\cdot$ is commutative: $xy=yx$
$^{-1}$ is an inverse: $xx^{-1}x=x$, $(x^{-1})^{-1}=x$
Morphisms
Let $\mathbf{S}$ and $\mathbf{T}$ be commutative inverse semigroups. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\rightarrow T$ that is a homomorphism:
$h(xy)=h(x)h(y)$, $h(x^{-1})=h(x)^{-1}$
Examples
Example 1:
Basic results
Properties
Finite members
$\begin{array}{lr} f(1)= &1\\ f(2)= &\\ f(3)= &\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ f(7)= &\\ \end{array}$
Subclasses
Superclasses
References
Trace: » commutative_inverse_semigroups