Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups

Gould, Victoria and Kambites, Mark (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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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 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User:	Ms Lucy van Russelt
Date Deposited:	30 Sep 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/619

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