On the structure of modules defined by subinjectivity

Altinay F., Buyukasik E., DURĞUN Y.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.18, sa.10, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 10
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1142/s0219498819501883
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Injective modules, subinjectivity domain, indigent modules, INJECTIVITY, RINGS, OPPOSITE, POOR
  • Çukurova Üniversitesi Adresli: Evet

Özet

The aim of this paper is to present new results and generalize some results about indigent modules. The commutative rings whose simple modules are indigent or injective are fully determined. The rings whose cyclic right modules are indigent are shown to be semisimple Artinian. We give a complete characterization of indigent modules over commutative hereditary Noetherian rings. We show that a reduced module is indigent if and only if it is a Whitehead test module for injectivity over commutative hereditary noetherian rings. Furthermore, Dedekind domains are characterized by test modules for injectivity by subinjectivity.