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

Victoria Gould; Mark Kambites

doi:10.1142/S0218196705002451

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

Victoria Gould, Mark Kambites

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	683-698
Number of pages	16
Journal	International Journal of Algebra and Computation
Volume	15
DOIs	https://doi.org/10.1142/S0218196705002451
Publication status	Published - 2005

Keywords

Algebra

Access to Document

10.1142/S0218196705002451

http://www-users.york.ac.uk/~varg1/amplenew.ps

Cite this

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title = "Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups.",

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.",

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T1 - Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups.

AU - Gould, Victoria

AU - Kambites, Mark

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N2 - 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.

AB - 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.

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DO - 10.1142/S0218196705002451

M3 - Article

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VL - 15

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EP - 698

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

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