CS-Baer and dual CS-Baer objects in abelian categories

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Crivei S., KESKİN TÜTÜNCÜ D., Radu S. M., Tribak R.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.22, no.10, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 10
  • Publication Date: 2023
  • Doi Number: 10.1142/s0219498823502201
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Abelian category, (dual) CS-Baer object, (dual) Baer object, (dual) CS-Rickart object, (dual) Rickart object, extending object, lifting object, module, STRONGLY RICKART OBJECTS, MODULES
  • Hacettepe University Affiliated: Yes

Abstract

We investigate relative CS-Baer objects in abelian categories in relationship with other relevant classes of objects such as relative Baer objects, extending objects, objects having certain summand intersection properties and relative CS-Rickart objects. Dual results are automatically obtained by applying the duality principle in abelian categories. We also study direct sums of relative CS-Baer objects, and we determine the complete structure of dual self-CS-Baer modules over Dedekind domains. Further applications are given to module categories.