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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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