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 | |