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inverse_semigroups [2010/07/29 15:46]
127.0.0.1 external edit
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(2)= &2\\ f(2)= &2\\
f(3)= &5\\ f(3)= &5\\
-f(4)= &52\\ +f(4)= &16\\ 
-f(5)= &208\\ +f(5)= &52\\ 
-f(6)= &911\\ +f(6)= &208\\ 
-f(7)= &\\+f(7)= &911\\ 
 +f(8)= &4637\\ 
 +f(9)= &26422\\ 
 +f(10)= &169163\\ 
 +f(11)= &1198651\\ 
 +f(12)= &9324047\\ 
 +f(13)= &78860687\\ 
 +f(14)= &719606005\\ 
 +f(15)= &7035514642\\
\end{array}$ \end{array}$
 +
 +http://oeis.org/A001428
====Subclasses==== ====Subclasses====