Inverse semigroups determined by their partial automorphism monoids
- Autores: Simon Goberstein
- Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 81, Nº 2, 2006, págs. 185-198
- Idioma: inglés
- DOI: 10.1017/s1446788700015810
- Enlaces
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Resumen
The partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental inverse semigroup $S$ with no isolated nontrivial subgroups is lattice determined `modulo semilattices' and if $T$ is an inverse semigroup whose partial automorphism monoid is isomorphic to that of $S$, then either $S$ and $T$ are isomorphic or they are dually isomorphic chains relative to the natural partial order; a similar result holds if $T$ is any semigroup and the inverse monoids consisting of all isomorphisms between subsemigroups of $S$ and $T$, respectively, are isomorphic. Moreover, for these results to hold, the conditions that $S$ be tightly connected and have no isolated nontrivial subgroups are essential.
