Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain
In this study, we investigate the projectivity domain of pure-projective modules. A pure-projective module is called special-pure-projective (s-pure-projective) module if its projectivity domain contains only regular modules. First, we describe all rings whose pure-projective modules are s-pure-proj...
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| Format: | Article |
| Language: | English |
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Naim Çağman
2024-06-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3789710 |
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| _version_ | 1849723759196372992 |
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| author | Zübeyir Türkoğlu |
| author_facet | Zübeyir Türkoğlu |
| author_sort | Zübeyir Türkoğlu |
| collection | DOAJ |
| description | In this study, we investigate the projectivity domain of pure-projective modules. A pure-projective module is called special-pure-projective (s-pure-projective) module if its projectivity domain contains only regular modules. First, we describe all rings whose pure-projective modules are s-pure-projective, and we show that every ring with an s-pure-projective module. Afterward, we research rings whose pure-projective modules are projective or s-pure-projective. Such rings are said to have $*$-property. We determine the right Noetherian rings have $*$-property. |
| format | Article |
| id | doaj-art-e35504e0292e428da268489c2fd16dc4 |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-e35504e0292e428da268489c2fd16dc42025-08-20T03:10:56ZengNaim ÇağmanJournal of New Theory2149-14022024-06-014711010.53570/jnt.14516622425Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity DomainZübeyir Türkoğlu0https://orcid.org/0000-0002-7852-8441DOKUZ EYLUL UNIVERSITYIn this study, we investigate the projectivity domain of pure-projective modules. A pure-projective module is called special-pure-projective (s-pure-projective) module if its projectivity domain contains only regular modules. First, we describe all rings whose pure-projective modules are s-pure-projective, and we show that every ring with an s-pure-projective module. Afterward, we research rings whose pure-projective modules are projective or s-pure-projective. Such rings are said to have $*$-property. We determine the right Noetherian rings have $*$-property.https://dergipark.org.tr/en/download/article-file/3789710projectivity domainpure-projective modules-pure-projective modulevon neumann regular ringsright goldie torsion rings |
| spellingShingle | Zübeyir Türkoğlu Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain Journal of New Theory projectivity domain pure-projective module s-pure-projective module von neumann regular rings right goldie torsion rings |
| title | Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain |
| title_full | Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain |
| title_fullStr | Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain |
| title_full_unstemmed | Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain |
| title_short | Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain |
| title_sort | rings whose pure projective modules have maximal or minimal projectivity domain |
| topic | projectivity domain pure-projective module s-pure-projective module von neumann regular rings right goldie torsion rings |
| url | https://dergipark.org.tr/en/download/article-file/3789710 |
| work_keys_str_mv | AT zubeyirturkoglu ringswhosepureprojectivemoduleshavemaximalorminimalprojectivitydomain |