On the classical zariski topology over prime spectrum of a module
| dc.authorscopusid | 57211853730 | |
| dc.authorscopusid | 7005541179 | |
| dc.contributor.author | Qeken S. | |
| dc.contributor.author | Alkan M. | |
| dc.date.accessioned | 2024-06-12T10:25:46Z | |
| dc.date.available | 2024-06-12T10:25:46Z | |
| dc.date.issued | 2017 | |
| dc.description.abstract | Let R be an associative ring with identity and Spec(M) denote the set of all prime submodules of a right R-module M. In this paper, we study the classical Zariski topology on Spec(M) which is denoted by ?c. We prove that if (Spec(M),?c) is a Noetherian topological space, then M has finitely many minimal prime submodules. We characterize all the irreducible components of (Spec(M),rc) and all the minimal prime submodules of M for a non-zero flat module M over a commutative ring R. We obtain some results concerning compactness and connectedness of (Spec(M),?c) by using algebraic properties of the module M. We give some equivalent conditions for (Spec(M),?c) to be a Hausdorff space or T1-space when M is a right module over a left perfect ring R. © 2017 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved. | en_US |
| dc.description.sponsorship | Akdeniz Üniversitesi; Consejo Nacional para Investigaciones Científicas y Tecnológicas, CONICIT | en_US |
| dc.description.sponsorship | The first author thanks the Scientific Technological Research Council of Turkey (TUBITAK) for the financial support. The second author was supported by the Scientific Research Project Administration of Akdeniz University. | en_US |
| dc.identifier.doi | 10.17777/pjms2017.20.4.595 | |
| dc.identifier.endpage | 604 | en_US |
| dc.identifier.issn | 1598-7264 | |
| dc.identifier.issue | 4 | en_US |
| dc.identifier.scopus | 2-s2.0-85075146332 | en_US |
| dc.identifier.scopusquality | Q3 | en_US |
| dc.identifier.startpage | 595 | en_US |
| dc.identifier.uri | https://doi.org/10.17777/pjms2017.20.4.595 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14551/16493 | |
| dc.identifier.volume | 20 | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Jangjeon Research Institute for Mathematical Sciences and Physics | en_US |
| dc.relation.ispartof | Proceedings of the Jangjeon Mathematical Society | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Classical Zariski Topology; Prime Spectrum; Prime Submodule | en_US |
| dc.title | On the classical zariski topology over prime spectrum of a module | en_US |
| dc.type | Article | en_US |
