Aufsatz in einer Fachzeitschrift
Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups
Details zur Publikation
Autor(inn)en: | Gould, V.; Kambites, M. |
Publikationsjahr: | 2005 |
Zeitschrift: | International Journal of Algebra and Computation |
Seitenbereich: | 683-698 |
Jahrgang/Band : | 15 |
Erste Seite: | 683 |
Letzte Seite: | 698 |
ISSN: | 0218-1967 |
Zusammenfassung, Abstract
We prove that any small cancellative category admits a faithful functor to a cancellative monoid. We use our result to show that any primitive ample semigroup is a full subsemigroup of a Rees matrix semigroup M-0 (M; I, I; P) where M is a cancellative monoid and P is the identity matrix. On the other hand a consequence of a recent result of Steinberg is that it is undecidable whether a finite ample semigroup embeds as a full subsemigroup of an inverse semigroup.
We prove that any small cancellative category admits a faithful functor to a cancellative monoid. We use our result to show that any primitive ample semigroup is a full subsemigroup of a Rees matrix semigroup M-0 (M; I, I; P) where M is a cancellative monoid and P is the identity matrix. On the other hand a consequence of a recent result of Steinberg is that it is undecidable whether a finite ample semigroup embeds as a full subsemigroup of an inverse semigroup.
