On rings with one middle class of injectivity domains

ALIZADE R. A. F. A. I. L., DEMIRCI Y. M., TURKMEN B. U. R. C. U. N. I. S. A. N. C. I., TURKMEN E. R. G. U. L.

MATHEMATICAL COMMUNICATIONS, cilt.27, sa.1, ss.109-126, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 1
  • Basım Tarihi: 2022
  • Dergi Adı: MATHEMATICAL COMMUNICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.109-126
  • Anahtar Kelimeler: injective module, poor module, modest module, SSI-ring, V-ring, WV-ring, Noetherian ring, POOR MODULES
  • Abdullah Gül Üniversitesi Adresli: Evet

Özet

A module M is said to be modest if the injectivity domain of M is the class of all crumbling modules. In this paper, we investigate the basic properties of modest modules. We provide characterizations of some classes of rings using modest modules. In particular, we show that a ring having the class of crumbling modules as the only right middle class of injectivity domains is either a right V-ring or right Noetherian; and a commutative ring with this property is regular. We also give criteria for a ring having the class of crumbling modules as the only right middle class of injectivity domains.