Subprojectivity domains of pure-projective modules

DURĞUN Y.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.19, sa.5, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 5
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1142/s0219498820500917
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Pure-projective module, subprojectivity domain, pp-indigent module, flat module, finitely saturated ring, RINGS, INJECTIVITY, FLAT
  • Çukurova Üniversitesi Adresli: Evet

Özet

In a recent paper, Holston et al. have defined a module M to be N-subprojective if for every epimorphism g : B -> N and homomorphism f : M -> N, there exists a homomorphism h : M -> B such that gh = f. Clearly, every module is subprojective relative to any projective module. For a module M, the subprojectivity domain of M is defined to be the collection of all modules N such that M is N-subprojective. We consider, for every pure-projective module M, the subprojective domain of M. We show that the flat modules are the only ones sharing the distinction of being in every single subprojectivity domain of pure-projective modules. Pure-projective modules whose subprojectivity domain is as small as possible will be called pure-projective indigent (pp-indigent). Properties of subprojectivity domains of pure-projective modules and of pp-indigent modules are studied. For various classes of modules (such as simple, cyclic, finitely generated and singular), necessary and sufficient conditions for the existence of pp-indigent modules of those types are studied. We characterize the structure of a Noetherian ring over which every (simple, cyclic, finitely generated) pure-projective module is projective or pp-indigent. Furthermore, finitely generated pp-indigent modules on commutative Noetherian hereditary rings are characterized.