Weak Rickart and dual weak Rickart objects in abelian categories

ABSTRACT

We introduce and investigate weak relative Rickart objects and dual weak relative Rickart objects in abelian categories. Several types of abelian categories are characterized in terms of (dual) weak relative Rickart properties. We relate our theory to the study of relative regular objects and (dual) relative Baer objects. We also give some applications to module and comodule categories.

KEYWORDS:

• Abelian category
• (dual) Baer object
• (dual) Rickart object
• (dual) weak Rickart object
• regular object
• spectral category

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 18E10
• 18E15
• 16D90
• 16T15

Acknowledgment

The authors would like to thank the referee for his / her nice comments on the paper.