Araştırma Makalesi
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Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain

Yıl 2024, Sayı: 47, 1 - 10, 30.06.2024

Zübeyir Türkoğlu

https://doi.org/10.53570/jnt.1451662

Öz

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.

Anahtar Kelimeler

Projectivity domain pure-projective module s-pure-projective module von Neumann regular rings right Goldie torsion rings

Kaynakça

  • C. Holston, S. R. Lopez-Permouth, N. O. Ertaş, Rings whose modules have maximal or minimal projectivity domain, Journal of Pure and Applied Algebra 216 (3) (2012) 673-678.
  • C. Holston, S. R. Lopez-Permouth, J. Mastromatteo, J. E. Simental-Rodriguez, An alternative perspective on projectivity of modules, Glasgow Mathematical Journal 57 (1) (2015) 83-99.
  • R. Alizade, D. D. Sipahi, Modules and abelian groups with minimal (pure-) projectivity domains, Journal of Algebra and Its Applications 16 (11) (2017) 1750203 13 pages.
  • R. Alizade, D. Dede Sipahi, Modules and abelian groups with a restricted domain of projectivity, Journal of Algebra and Its Applications (2024) 2550173.
  • N. Er, S. Lopez-Permouth, N. Sökmez, Rings whose modules have maximal or minimal injectivity domains, Journal of Algebra 330 (2011) 404-417.
  • N. O. Ertaş, R. Tribak, Some variations of projectivity, Journal of Algebra and Its Applications 21 (12) (2022) 2250236 19 pages.
  • S. Crivei, R. Pop, Projectivity and subprojectivity domains in exact categories, Journal of Algebra and Its Applications (2023) 2550134.
  • D. Bennis, J. R. Garcia Rozas, H. Ouberka, L. Oyonarte, A new approach to projectivity in the categories of complexes, Annali di Matematica Pura ed Applicata 201 (2022) 2871-2889.
  • H. Amzil, D. Bennis, J. R. Garcia Rozas, H. Ouberka, L. Oyonarte, Subprojectivity in abelian categories, Applied Categorical Structures 29 (5) (2021) 889-913.
  • Y. Alagöz, Y. Durğun, An alternative perspective on pure-projectivity of modules, Sao Paulo Journal of Mathematical Sciences 14 (2) (2020) 631-650.
  • Y. Alagöz, Weakly poor modules, Konuralp Journal of Mathematics 10 (2) (2022) 250-254.
  • Y. Durğun, RD-projective module whose subprojectivity domain is minimal, Hacettepe Journal of Mathematics and Statistics 51 (2) (2022) 373-382.
  • Y. Durğun, The opposite of projectivity by proper classes, Journal of Algebra and Its Application (2023) 2450172.
  • Y. Durğun, Ş. Kalir, A. Y. Shibeshi, On projectivity of finitely generated modules, Communications in Algebra 51 (9) (2023) 3623-3631.
  • Y. Durğun, A. Çobankaya, On subprojectivity domains of g-semiartinian modules, Journal of Algebra and Its Applications 20 (7) (2021) 2150119 15 pages.
  • F. W. Anderson, K. R. Fuller, Rings and categories of modules, Springer, New York, 1992.
  • R. Wisbauer, Foundations of module and ring theory, Gordon and Breach, Reading, 1991.
  • T. Y. Lam, Lectures on modules and rings, Vol. 189 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1999.
  • K. R. Goodearl, Singular torsion and the splitting properties, Vol. 124 of American Mathematical Society, 1972.

Yıl 2024, Sayı: 47, 1 - 10, 30.06.2024

Zübeyir Türkoğlu

https://doi.org/10.53570/jnt.1451662

Öz

Kaynakça

  • C. Holston, S. R. Lopez-Permouth, N. O. Ertaş, Rings whose modules have maximal or minimal projectivity domain, Journal of Pure and Applied Algebra 216 (3) (2012) 673-678.
  • C. Holston, S. R. Lopez-Permouth, J. Mastromatteo, J. E. Simental-Rodriguez, An alternative perspective on projectivity of modules, Glasgow Mathematical Journal 57 (1) (2015) 83-99.
  • R. Alizade, D. D. Sipahi, Modules and abelian groups with minimal (pure-) projectivity domains, Journal of Algebra and Its Applications 16 (11) (2017) 1750203 13 pages.
  • R. Alizade, D. Dede Sipahi, Modules and abelian groups with a restricted domain of projectivity, Journal of Algebra and Its Applications (2024) 2550173.
  • N. Er, S. Lopez-Permouth, N. Sökmez, Rings whose modules have maximal or minimal injectivity domains, Journal of Algebra 330 (2011) 404-417.
  • N. O. Ertaş, R. Tribak, Some variations of projectivity, Journal of Algebra and Its Applications 21 (12) (2022) 2250236 19 pages.
  • S. Crivei, R. Pop, Projectivity and subprojectivity domains in exact categories, Journal of Algebra and Its Applications (2023) 2550134.
  • D. Bennis, J. R. Garcia Rozas, H. Ouberka, L. Oyonarte, A new approach to projectivity in the categories of complexes, Annali di Matematica Pura ed Applicata 201 (2022) 2871-2889.
  • H. Amzil, D. Bennis, J. R. Garcia Rozas, H. Ouberka, L. Oyonarte, Subprojectivity in abelian categories, Applied Categorical Structures 29 (5) (2021) 889-913.
  • Y. Alagöz, Y. Durğun, An alternative perspective on pure-projectivity of modules, Sao Paulo Journal of Mathematical Sciences 14 (2) (2020) 631-650.
  • Y. Alagöz, Weakly poor modules, Konuralp Journal of Mathematics 10 (2) (2022) 250-254.
  • Y. Durğun, RD-projective module whose subprojectivity domain is minimal, Hacettepe Journal of Mathematics and Statistics 51 (2) (2022) 373-382.
  • Y. Durğun, The opposite of projectivity by proper classes, Journal of Algebra and Its Application (2023) 2450172.
  • Y. Durğun, Ş. Kalir, A. Y. Shibeshi, On projectivity of finitely generated modules, Communications in Algebra 51 (9) (2023) 3623-3631.
  • Y. Durğun, A. Çobankaya, On subprojectivity domains of g-semiartinian modules, Journal of Algebra and Its Applications 20 (7) (2021) 2150119 15 pages.
  • F. W. Anderson, K. R. Fuller, Rings and categories of modules, Springer, New York, 1992.
  • R. Wisbauer, Foundations of module and ring theory, Gordon and Breach, Reading, 1991.
  • T. Y. Lam, Lectures on modules and rings, Vol. 189 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1999.
  • K. R. Goodearl, Singular torsion and the splitting properties, Vol. 124 of American Mathematical Society, 1972.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Araştırma Makalesi
Yazarlar

Zübeyir Türkoğlu 0000-0002-7852-8441

Yayımlanma Tarihi 30 Haziran 2024
Gönderilme Tarihi 12 Mart 2024
Kabul Tarihi 2 Mayıs 2024
Yayımlandığı Sayı Yıl 2024 Sayı: 47

Kaynak Göster

APA Türkoğlu, Z. (2024). Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain. Journal of New Theory(47), 1-10. https://doi.org/10.53570/jnt.1451662
AMA Türkoğlu Z. Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain. JNT. Haziran 2024;(47):1-10. doi:10.53570/jnt.1451662
Chicago Türkoğlu, Zübeyir. “Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain”. Journal of New Theory, sy. 47 (Haziran 2024): 1-10. https://doi.org/10.53570/jnt.1451662.
EndNote Türkoğlu Z (01 Haziran 2024) Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain. Journal of New Theory 47 1–10.
IEEE Z. Türkoğlu, “Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain”, JNT, sy. 47, ss. 1–10, Haziran 2024, doi: 10.53570/jnt.1451662.
ISNAD Türkoğlu, Zübeyir. “Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain”. Journal of New Theory 47 (Haziran 2024), 1-10. https://doi.org/10.53570/jnt.1451662.
JAMA Türkoğlu Z. Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain. JNT. 2024;:1–10.
MLA Türkoğlu, Zübeyir. “Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain”. Journal of New Theory, sy. 47, 2024, ss. 1-10, doi:10.53570/jnt.1451662.
Vancouver Türkoğlu Z. Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain. JNT. 2024(47):1-10.
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