Journal article
Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups
Publication Details
Authors: | Gould, V.; Kambites, M. |
Publication year: | 2005 |
Journal: | International Journal of Algebra and Computation |
Pages range : | 683-698 |
Volume number: | 15 |
Start page: | 683 |
End page: | 698 |
ISSN: | 0218-1967 |
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.
