Strongly CS-Rickart and dual strongly CS-Rickart objects in abelian categories
Septimu Crivei, Simona Maria Radu
TL;DR
This paper introduces the concepts of strongly CS-Rickart and dual strongly CS-Rickart objects in abelian categories, generalizing existing notions and exploring their properties and structural behaviors.
Contribution
It presents new definitions of strongly CS-Rickart objects in abelian categories and analyzes their properties, including behavior under direct summands and (co)products.
Findings
Defined strongly CS-Rickart and dual strongly CS-Rickart objects.
Established properties and structural results for these objects.
Analyzed classes where all objects are strongly self-CS-Rickart.
Abstract
We introduce (dual) strongly relative CS-Rickart objects in abelian categories, as common generalizations of (dual) strongly relative Rickart objects and strongly extending (lifting) objects. We give general properties, and we study direct summands, (co)products of (dual) strongly relative CS-Rickart objects and classes all of whose objects are (dual) strongly self-CS-Rickart.
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