Rings with singular modules having a restricted subprojectivity domain

ÇOBANKAYA A., Shibeshi A. Y., Sönmez R.

Sao Paulo Journal of Mathematical Sciences, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s40863-024-00442-7
  • Dergi Adı: Sao Paulo Journal of Mathematical Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: 16D10, 16D40, Goldie torsion modules, Gp-indigent module, Nonsingular ring, Subprojective domain
  • Çukurova Üniversitesi Adresli: Evet

Özet

Given modules X and Y, X is said to be Y-subprojective if for every epimorphism π:P→Y and every homomorphism α:X→Y, there exists a homomorphism γ:X→P such that πγ=α. For a module X, the subprojectivity domain of X is defined to be the collection of all modules Y such that X is Y-subprojective. The class of ec-flat modules is the smallest possible subprojectivity domain of a goldie torsion module. In this paper, we consider goldie torsion modules whose subprojectivty domains contain only ec-flat modules, and we referred to these modules as gb-indigent.We investigate the rings over which every goldie torsion (singular, simple) module is either projective (ec-flat) or gp-indigent. Furthermore, gp-indigent modules on right nonsingular rings are characterized.