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inverse_semigroups [2016/12/02 08:15]
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====