CS-Rickart and dual CS-Rickart objects in abelian categories
Septimiu Crivei, Simona Maria Radu
TL;DR
This paper introduces and studies (dual) relative CS-Rickart objects in abelian categories, generalizing existing concepts and exploring their properties, with applications to Grothendieck, module, and comodule categories.
Contribution
It defines (dual) relative CS-Rickart objects, extends existing concepts, and analyzes their properties and applications in various categories.
Findings
Characterization of (dual) relative CS-Rickart objects
Analysis of direct summands and (co)products
Applications to module and comodule categories
Abstract
We introduce (dual) relative CS-Rickart objects in abelian categories, as common generalizations of (dual) relative Rickart objects and extending (lifting) objects. We study direct summands and (co)products of (dual) relative CS-Rickart objects as well as classes all of whose objects are (dual) self-CS-Rickart. Applications are given to Grothendieck categories and, in particular, to module and comodule categories.
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Taxonomy
TopicsRings, Modules, and Algebras · Protein Degradation and Inhibitors