Irreducibility and Primality in Differentiability Classes
| dc.contributor.author | Batal, Ahmet | |
| dc.contributor.author | Eyidoğan, S. | |
| dc.contributor.author | Göral, Haydar | |
| dc.date.accessioned | 2023-04-19T12:39:44Z | |
| dc.date.available | 2023-04-19T12:39:44Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | In this note, we give criteria for the irreducibility of functions in Cm [0, 1], where m ∈ {1, 2, 3, ...} ∪ {∞} ∪ {ω}. We also discuss irreducibility in multivariable differentiability classes. Moreover, we characterize irreducible functions and maximal ideals in C∞ [0, 1]. In fact, irreducible and prime smooth functions are the same, and every maximal ideal of C∞ [0, 1] is principal. © 2023 Michigan State University Press. All rights reserved. | en_US |
| dc.description.sponsorship | The authors would like to thank the referee for many valuable comments which immensely improved the quality of the manuscript. | en_US |
| dc.identifier.doi | 10.14321/realanalexch.48.1.1660633299 | |
| dc.identifier.issn | 0147-1937 | |
| dc.identifier.scopus | 2-s2.0-85152099098 | |
| dc.identifier.uri | https://doi.org/10.14321/realanalexch.48.1.1660633299 | |
| dc.identifier.uri | https://hdl.handle.net/11147/13390 | |
| dc.language.iso | en | en_US |
| dc.publisher | Michigan State University Press | en_US |
| dc.relation.ispartof | Real Analysis Exchange | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Differentiability classes | en_US |
| dc.subject | Irreducibility | en_US |
| dc.subject | Maximal and prime ideals | en_US |
| dc.title | Irreducibility and Primality in Differentiability Classes | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication | |
| gdc.author.institutional | Batal, Ahmet | |
| gdc.author.institutional | Göral, Haydar | |
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| gdc.description.department | İzmir Institute of Technology. Mathematics | en_US |
| gdc.description.departmenttemp | Batal, A., Department of Mathematics, Izmir Institute of Technology, Urla, Izmir, 35430, Turkey; Eyidogan, S., Department of Mathematics, Faculty of Science, Çukurova University, Adana, 01330, Turkey; Göral, H., Department of Mathematics, Izmir Institute of Technology, Urla, Izmir, 35430, Turkey | en_US |
| gdc.description.endpage | 138 | en_US |
| gdc.description.issue | 1 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q4 | |
| gdc.description.startpage | 119 | en_US |
| gdc.description.volume | 48 | en_US |
| gdc.description.wosquality | Q4 | |
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