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.

Last updated on 2019-01-11 at 16:05