Some Results on Simple-Direct-Injective Modules

KESKİN TÜTÜNCÜ D., Tribak R.

KYUNGPOOK MATHEMATICAL JOURNAL, cilt.63, sa.4, ss.521-537, 2023 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 63 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.5666/kmj.2023.63.4.521
  • Dergi Adı: KYUNGPOOK MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.521-537
  • Hacettepe Üniversitesi Adresli: Evet

Özet

A module M is called a simple-direct-injective module if, whenever A and B are simple submodules of M with A similar to= B and B is a direct summand of M, then A is a direct summand of M. Some new characterizations of these modules are proved. The structure of simple-direct-injective modules over a commutative Dedekind domain is fully determined. Also, some relevant counterexamples are indicated to show that a left simpledirect-injective ring need not be right simple-direct-injective.