dc.contributor.author Madsen, Dag Oskar dc.contributor.author Marczinzik, Rene dc.date.accessioned 2019-02-04T13:26:12Z dc.date.available 2019-02-04T13:26:12Z dc.date.created 2019-01-17T15:02:23Z dc.date.issued 2018 dc.identifier.citation Madsen, D. O. & Marczinzik, R. (2018). On bounds of homological dimensions in Nakayama algebras. Proceedings of the American Mathematical Society, Series B, 5, 40-49. doi: nb_NO dc.identifier.issn 2330-1511 dc.identifier.uri http://hdl.handle.net/11250/2583774 dc.description.abstract Let $A$ be a Nakayama algebra with $n$ simple modules and a simple module $S$ of even projective dimension. Choose $m$ minimal such that a simple $A$-module with projective dimension $2m$ exists. Then we show that the global dimension of $A$ is bounded by $n+m-1$. This gives a combined generalisation of results of Gustafson [J. Algebra 97 (1985), pp. 14-16] and Madsen [Projective dimensions and Nakayama algebras, Amer. Math. Soc., Providence, RI, 2005]. In [Comm. Algebra 22 (1994), pp. 1271-1280], Brown proved that the global dimension of quasi-hereditary Nakayama algebras with $n$ simple modules is bounded by $n$. Using our result on the bounds of global dimensions of Nakayama algebras, we give a short new proof of this result and generalise Brown's result from quasi-hereditary to standardly stratified Nakayama algebras, where the global dimension is replaced with the finitistic dimension. nb_NO dc.language.iso eng nb_NO dc.rights Navngivelse-Ikkekommersiell 4.0 Internasjonal * dc.rights.uri http://creativecommons.org/licenses/by-nc/4.0/deed.no * dc.title On bounds of homological dimensions in Nakayama algebras nb_NO dc.type Journal article nb_NO dc.type Peer reviewed nb_NO dc.description.version publishedVersion nb_NO dc.rights.holder © 2018, The Author(s) nb_NO dc.subject.nsi VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414 nb_NO dc.source.pagenumber 40-49 nb_NO dc.source.volume 5 nb_NO dc.source.journal Proceedings of the American Mathematical Society, Series B nb_NO dc.identifier.doi 10.1090/bproc/36 dc.identifier.cristin 1659550
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