On the Upper Dual Zariski Topology
| dc.contributor.author | Ceken, Secil | |
| dc.date.accessioned | 2024-06-12T11:13:58Z | |
| dc.date.available | 2024-06-12T11:13:58Z | |
| dc.date.issued | 2020 | |
| dc.department | Trakya Üniversitesi | en_US |
| dc.description | 1st Mediterranean International Conference of Pure and Applied Mathematics and Related Areas (MICOPAM) -- OCT 26-29, 2018 -- Akdeniz Univ, Antalya, TURKEY | en_US |
| dc.description.abstract | Let R be a ring with identity and M be a left R-module. The set of all second submodules of M is called the second spectrum of M and denoted by Spec(s)(M). For each prime ideal p of R we define Spec(p)(s)(M) := {S is an element of Spec(s)(M) : ann(R)(S) = p g. A second submodule Q ofMis called an upper second submodule if there exists a prime ideal p of R such that Spec(p)(s)(M)not equal (sic) and Q = Sigma S is an element of Spec(p)(s)(M) S. The set of all upper second submodules ofMis called upper second spectrumofMand denoted by u:Specs(M). In this paper, we discuss the relationships between various algebraic properties of M and the topological conditions on u:Spec(s)(M) with the dual Zarsiki topology. Also, we topologize u:Specs(M) with the patch topology and the finer patch topology. We show that for every left R-moduleM, u:Spec(s)(M) with the finer patch topology is a Hausdorff, totally disconnected space and if M is Artinian then u:Spec(s)(M) is a compact space with the patch and finer patch topology. Finally, by applying Hochster's characterization of a spectral space, we show that if M is an Artinian left R-module, then u:Specs(M) with the dual Zariski topology is a spectral space. | en_US |
| dc.identifier.doi | 10.2298/FIL2002483C | |
| dc.identifier.endpage | 489 | en_US |
| dc.identifier.issn | 0354-5180 | |
| dc.identifier.issue | 2 | en_US |
| dc.identifier.scopus | 2-s2.0-85096963623 | en_US |
| dc.identifier.scopusquality | Q3 | en_US |
| dc.identifier.startpage | 483 | en_US |
| dc.identifier.uri | https://doi.org/10.2298/FIL2002483C | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14551/23755 | |
| dc.identifier.volume | 34 | en_US |
| dc.identifier.wos | WOS:000595329700022 | en_US |
| dc.identifier.wosquality | Q3 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Univ Nis, Fac Sci Math | en_US |
| dc.relation.ispartof | Filomat | en_US |
| dc.relation.publicationcategory | Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Second Submodule | en_US |
| dc.subject | Upper Second Submodule | en_US |
| dc.subject | Dual Zariski Topology | en_US |
| dc.subject | Patch Topology | en_US |
| dc.subject | Spectral Space | en_US |
| dc.subject | Prime Spectrum | en_US |
| dc.subject | 2nd Spectrum | en_US |
| dc.subject | Module | en_US |
| dc.subject | Notion | en_US |
| dc.title | On the Upper Dual Zariski Topology | en_US |
| dc.type | Conference Object | en_US |
