Differences
This shows you the differences between two versions of the page.
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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 | ||
| Line 27: | Line 27: | ||
| ====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==== | ||
| Line 57: | Line 61: | ||
| 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}$ | ||
Trace:
