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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====