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

TL;DR

This paper explores the properties and relationships of relative CS-Baer objects in abelian categories, including duality, direct sums, and specific module structures, with applications to module theory.

Contribution

It introduces the concept of relative CS-Baer objects in abelian categories and analyzes their properties, duality, and structure, especially over Dedekind domains.

Findings

Characterization of dual self-CS-Baer modules over Dedekind domains

Relationships between relative CS-Baer and other object classes in abelian categories

Structural results on direct sums of relative CS-Baer objects

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.