Files in this item
Presentations for subrings and subalgebras of finite co-rank
Item metadata
dc.contributor.author | Mayr, Peter | |
dc.contributor.author | Ruskuc, Nikola | |
dc.date.accessioned | 2020-12-07T15:53:26Z | |
dc.date.available | 2020-12-07T15:53:26Z | |
dc.date.issued | 2020-03 | |
dc.identifier | 260242077 | |
dc.identifier | 4590dccb-e6b0-4dce-b12e-9978955c1b74 | |
dc.identifier | 85084033775 | |
dc.identifier | 000536511600003 | |
dc.identifier.citation | Mayr , P & Ruskuc , N 2020 , ' Presentations for subrings and subalgebras of finite co-rank ' , Quarterly Journal of Mathematics , vol. 71 , no. 1 , pp. 53-71 . https://doi.org/10.1093/qmathj/haz033 | en |
dc.identifier.issn | 0033-5606 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/73702036 | |
dc.identifier.uri | https://hdl.handle.net/10023/21068 | |
dc.description.abstract | Let K be a commutative Noetherian ring with identity, let A be a K-algebra and let B be a subalgebra of A such that A/B is finitely generated as a K-module. The main result of the paper is that A is finitely presented (resp. finitely generated) if and only if B is finitely presented (resp. finitely generated). As corollaries, we obtain: a subring of finite index in a finitely presented ring is finitely presented; a subalgebra of finite co-dimension in a finitely presented algebra over a field is finitely presented (already shown by Voden in 2009). We also discuss the role of the Noetherian assumption on K and show that for finite generation it can be replaced by a weaker condition that the module A/B be finitely presented. Finally, we demonstrate that the results do not readily extend to non-associative algebras, by exhibiting an ideal of co-dimension 1 of the free Lie algebra of rank 2 which is not finitely generated as a Lie algebra. | |
dc.format.extent | 19 | |
dc.format.extent | 308720 | |
dc.language.iso | eng | |
dc.relation.ispartof | Quarterly Journal of Mathematics | en |
dc.subject | Ring | en |
dc.subject | K-algebra | en |
dc.subject | Finitely presented | en |
dc.subject | Finitely generated | en |
dc.subject | Subalgebra | en |
dc.subject | Free algebra | en |
dc.subject | Reidemeister-Schreier | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject.lcc | QA | en |
dc.title | Presentations for subrings and subalgebras of finite co-rank | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | 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.identifier.doi | 10.1093/qmathj/haz033 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1709.04435 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.