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Generators and presentations for direct and wreath products of monoid acts
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dc.contributor.author | Miller, Craig | |
dc.date.accessioned | 2018-12-20T11:30:09Z | |
dc.date.available | 2018-12-20T11:30:09Z | |
dc.date.issued | 2018-12-17 | |
dc.identifier.citation | Miller , C 2018 , ' Generators and presentations for direct and wreath products of monoid acts ' , Semigroup Forum , vol. First Online . https://doi.org/10.1007/s00233-018-9987-5 | en |
dc.identifier.issn | 0037-1912 | |
dc.identifier.other | PURE: 256910096 | |
dc.identifier.other | PURE UUID: a643d7ba-c3c5-444f-9358-153b5f2e2c6d | |
dc.identifier.other | Scopus: 85058711912 | |
dc.identifier.other | WOS: 000511555500014 | |
dc.identifier.uri | https://hdl.handle.net/10023/16736 | |
dc.description | The author would like to thank the EPSRC for financial support. | en |
dc.description.abstract | We investigate the preservation of the properties of being finitely generated and finitely presented under both direct and wreath products of monoid acts. A monoid M is said to preserve property P in direct products if, for any two M-acts A and B, the direct product A x B has property P if and only if both A and B have property P. It is proved that the monoids M that preserve finite generation (resp. finitely presentability) in direct products are precisely those for which the diagonal M-act M x M is finitely generated (resp. finitely presented). We show that a wreath product A ≀ B is finitely generated if and only if both A and B are finitely generated. It is also proved that a necessary condition for A ≀ B to be finitely presented is that both A and B are finitely presented. Finally, we find some sufficient conditions for a wreath product to be finitely presented. | |
dc.format.extent | 24 | |
dc.language.iso | eng | |
dc.relation.ispartof | Semigroup Forum | en |
dc.rights | © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | en |
dc.subject | Monoid act | en |
dc.subject | Presentation | en |
dc.subject | Direct product | en |
dc.subject | Wreath product | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Generators and presentations for direct and wreath products of monoid acts | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1007/s00233-018-9987-5 | |
dc.description.status | Peer reviewed | en |
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