The Infinitude of the Primes and Some Coloring Theorems
| dc.contributor.author | Adibelli, Azem Berivan | |
| dc.contributor.author | Goral, Haydar | |
| dc.date.accessioned | 2025-08-27T16:40:01Z | |
| dc.date.available | 2025-08-27T16:40:01Z | |
| dc.date.issued | 2025 | |
| dc.description.abstract | We first prove the infinitude of the primes via a special case of Rado's theorem whose proof is based on the infinite Ramsey theorem. In the proof, we use the colorings of the positive integers introduced by Levent Alpoge [1] and Andrew Granville [2]. Finally, using Rado's theorem for integral domains, we will give another proof for the infinitude of nonassociated prime elements in any unique factorization domain R with a few units. | en_US |
| dc.description.sponsorship | Scientific and Technological Research Council of Turkey (TUBITAK) [122F027] | en_US |
| dc.description.sponsorship | This work is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) with the project number 122F027, and it is carried out by the second author. We are deeply grateful to Mauro Di Nasso for sharing Theorem 11 with us. The authors would like to thank the referee and the editor for many valuable comments which immensely improved the quality of the manuscript. | en_US |
| dc.identifier.doi | 10.1080/00029890.2025.2525049 | |
| dc.identifier.issn | 0002-9890 | |
| dc.identifier.issn | 1930-0972 | |
| dc.identifier.scopus | 2-s2.0-105012521634 | |
| dc.identifier.uri | https://doi.org/10.1080/00029890.2025.2525049 | |
| dc.identifier.uri | https://hdl.handle.net/11147/18378 | |
| dc.language.iso | en | en_US |
| dc.publisher | Taylor & Francis inc | en_US |
| dc.relation.ispartof | American Mathematical Monthly | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.title | The Infinitude of the Primes and Some Coloring Theorems | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication | |
| gdc.author.scopusid | 60028972000 | |
| gdc.author.scopusid | 55616260000 | |
| gdc.coar.type | text::journal::journal article | |
| gdc.description.department | İzmir Institute of Technology | en_US |
| gdc.description.departmenttemp | [Adibelli, Azem Berivan; Goral, Haydar] Izmir Inst Technol, Fac Sci, Dept Math, TR-35430 Izmir, Turkiye | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q4 | |
| gdc.description.woscitationindex | Science Citation Index Expanded | |
| gdc.description.wosquality | Q4 | |
| gdc.identifier.wos | WOS:001543864200001 | |
| gdc.index.type | WoS | |
| gdc.index.type | Scopus | |
| relation.isAuthorOfPublication.latestForDiscovery | 9c9e85f7-1109-4fca-b449-2f03ed2c74c2 | |
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