2006.383: Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups
2006.383: Victoria Gould and Mark Kambites (2005) Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups. International Journal of Algebra and Computation, 15 (4). pp. 683-698. ISSN 0218-1967
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DOI: 10.1142/S0218196705002451
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 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Cancellative category; abundant semigroup; ample semigroup; primitive idempotents |
| Subjects: | MSC 2000 > 18 Category theory; homological algebra MSC 2000 > 20 Group theory and generalizations |
| MIMS number: | 2006.383 |
| Deposited By: | Miss Louise Stait |
| Deposited On: | 30 September 2006 |
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