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inverse_semigroups [2016/12/02 08:13]
jipsen
inverse_semigroups [2016/12/02 08:34] (current)
jipsen
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-$^{-1}$ is an inverse:  $xx^{-1}x=x$, $(x^{-1})^{-1}=x$+$^{-1}$ is an inverse:  $xx^{-1}x=x$ and $(x^{-1})^{-1}=x$
-idempotents commute:  $xx^{-1}y^{-1}y=y^{-1}yxx^{-1}$+idempotents commute:  $xx^{-1}yy^{-1}=yy^{-1}xx^{-1}$
==Morphisms== ==Morphisms==
Let $\mathbf{S}$ and $\mathbf{T}$ be inverse semigroups. A morphism from Let $\mathbf{S}$ and $\mathbf{T}$ be inverse semigroups. A morphism from
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====Basic results==== ====Basic results====
 +
 +$x*x=x \implies \exists y\ x=y*y^{-1}$
 +
 +$\forall x\exists y\ xx^{-1}=y^{-1}y$
====Properties==== ====Properties====
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f(7)= &911\\ f(7)= &911\\
f(8)= &4637\\ f(8)= &4637\\
-f(8)= &26422\\ +f(9)= &26422\\ 
-f(8)= &169163\\ +f(10)= &169163\\ 
-f(8)= &1198651\\ +f(11)= &1198651\\ 
-f(8)= &9324047\\ +f(12)= &9324047\\ 
-f(8)= &78860687\\ +f(13)= &78860687\\ 
-f(8)= &719606005\\ +f(14)= &719606005\\ 
-f(8)= &7035514642\\+f(15)= &7035514642\\
\end{array}$ \end{array}$