The Krull dimension-dependent elements of a Noetherian commutative ring
| dc.contributor.author | Babaei, S. | |
| dc.contributor.author | Sevim, E. Sengelen | |
| dc.date.accessioned | 2024-07-18T20:48:48Z | |
| dc.date.available | 2024-07-18T20:48:48Z | |
| dc.date.issued | 2024 | |
| dc.department | İstanbul Bilgi Üniversitesi | en_US |
| dc.description.abstract | In this paper, we introduce the Krull dimension-dependent elements of a Noetherian commutative ring. Let x, y be non-unit elements of a commutative ring R. x, y are called Krull dimension-dependent elements, whenever dim R/(Rx + Ry) = min{dim R/Rx, dim R/Ry}. We investigate the elements of a ring according to this property. Among the many results, we characterize the rings that all elements of them are Krull dimension-dependent and we call them, closed under the Krull dimension. Moreover, we determine the structure of the rings with Krull dimension at most 1. that are closed under the Krull dimension. | en_US |
| dc.identifier.doi | 10.1142/S0219498824500269 | |
| dc.identifier.issn | 0219-4988 | |
| dc.identifier.issn | 1793-6829 | |
| dc.identifier.issue | 2 | en_US |
| dc.identifier.scopus | 2-s2.0-85143635647 | en_US |
| dc.identifier.scopusquality | Q2 | en_US |
| dc.identifier.uri | https://doi.org/10.1142/S0219498824500269 | |
| dc.identifier.uri | https://hdl.handle.net/11411/7931 | |
| dc.identifier.volume | 23 | en_US |
| dc.identifier.wos | WOS:000874497000004 | 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 | World Scientific Publ Co Pte Ltd | en_US |
| dc.relation.ispartof | Journal of Algebra and Its Applications | 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 | Krull Dimension-Dependent Elements | en_US |
| dc.subject | Closed Under The Krull Dimension | en_US |
| dc.subject | Associated Prime İdeals | en_US |
| dc.title | The Krull dimension-dependent elements of a Noetherian commutative ring | |
| dc.type | Article |
