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On finitary properties for fiber products of free semigroups and free monoids
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dc.contributor.author | Clayton, Ashley | |
dc.date.accessioned | 2020-08-18T08:30:06Z | |
dc.date.available | 2020-08-18T08:30:06Z | |
dc.date.issued | 2020-08-14 | |
dc.identifier.citation | Clayton , A 2020 , ' On finitary properties for fiber products of free semigroups and free monoids ' , Semigroup Forum , vol. First Online . https://doi.org/10.1007/s00233-020-10127-0 | en |
dc.identifier.issn | 0037-1912 | |
dc.identifier.other | PURE: 269446538 | |
dc.identifier.other | PURE UUID: b914ccfe-6cce-45a5-b0a3-1e9f7ab1dc96 | |
dc.identifier.other | Scopus: 85089366225 | |
dc.identifier.other | WOS: 000559704400001 | |
dc.identifier.uri | https://hdl.handle.net/10023/20480 | |
dc.description.abstract | We consider necessary and sufficient conditions for finite generation and finite presentability for fiber products of free semigroups and free monoids. We give a necessary and sufficient condition on finite fiber quotients for a fiber product of two free monoids to be finitely generated, and show that all such fiber products are also finitely presented. By way of contrast, we show that fiber products of free semigroups over finite fiber quotients are never finitely generated. We then consider fiber products of free semigroups over infinite semigroups, and show that for such a fiber product to be finitely generated, the quotient must be infinite but finitely generated, idempotent-free, and J-trivial. Finally, we construct automata accepting the indecomposable elements of the fiber product of two free monoids/semigroups over free monoid/semigroup fibers, and give a necessary and sufficient condition for such a product to be finitely generated. | |
dc.format.extent | 32 | |
dc.language.iso | eng | |
dc.relation.ispartof | Semigroup Forum | en |
dc.rights | Copyright © The Author(s) 2020. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | en |
dc.subject | Subdirect product | en |
dc.subject | Fiber product | en |
dc.subject | Semigroup | en |
dc.subject | Free semigroup | en |
dc.subject | Free monoid | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On finitary properties for fiber products of free semigroups and free monoids | 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/s00233-020-10127-0 | |
dc.description.status | Peer reviewed | en |
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