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Subalgebras of FA-presentable algebras
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dc.contributor.author | Cain, A.J. | |
dc.contributor.author | Ruskuc, Nik | |
dc.date.accessioned | 2015-06-20T23:10:30Z | |
dc.date.available | 2015-06-20T23:10:30Z | |
dc.date.issued | 2014-06 | |
dc.identifier.citation | Cain , A J & Ruskuc , N 2014 , ' Subalgebras of FA-presentable algebras ' , Algebra Universalis . https://doi.org/10.1007/s00012-014-0293-0 | en |
dc.identifier.issn | 0002-5240 | |
dc.identifier.other | PURE: 106033402 | |
dc.identifier.other | PURE UUID: 3e1c8e2b-f52b-47d2-895b-5295ed45d8df | |
dc.identifier.other | Scopus: 84908147785 | |
dc.identifier.other | WOS: 000341907700001 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/73702065 | |
dc.identifier.uri | https://hdl.handle.net/10023/6852 | |
dc.description.abstract | Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable. | |
dc.format.extent | 23 | |
dc.language.iso | eng | |
dc.relation.ispartof | Algebra Universalis | en |
dc.rights | © Springer Basel 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/s00012-014-0293-0 | en |
dc.subject | Automatic presentations | en |
dc.subject | FA-presentations | en |
dc.subject | Algebras | en |
dc.subject | Finitely generated subalgebras | en |
dc.subject | Unary | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Subalgebras of FA-presentable algebras | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.sponsor | EPSRC | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. School of Mathematics and Statistics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1007/s00012-014-0293-0 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2015-06-21 | |
dc.identifier.grantnumber | EP/H011978/1 | en |
dc.identifier.grantnumber | EP/J006440/1 | en |
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