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.