Purely Rickart and dual purely Rickart objects in Grothendieck categories
type: Item
instance of: scholarly article
title: Purely Rickart and dual purely Rickart objects in Grothendieck categories
zbMATH Open document ID: 1476.18003
author: Sultan Eylem Toksoy
published in: Mediterranean Journal of Mathematics
publication date: 2021-09-20T00:00:00Z
review text: The paper deals with a generalization of the notion of Rickart modules and their duals for Grothendieck categories. More precisely, the author defines the notions of purely Rickart objects and their duals, and studies their main properties. For instance, it is shown in Corollary 3.7 that every purely self-Rickart object has the direct pure intersection property. In addition, the author uses the new notion to characterize when a locally finitely generated Grothendieck categories is regular (Theorem 5.1). This happens if and only if every object is purely self-Rickart. The author also considers relative purely Baer objects in Grothendieck categories and use the results on Rickart objects to study them. Finally, several applications in concrete Grothendieck categories, like module categories and comodule categories are provided.
reviewed by: S. Estrada
Mathematics Subject Classification ID: 18E10
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16T15
zbMATH DE Number: 7397614
zbMATH Keywords: abelian category
zbMATH Keywords: Grothendieck category
zbMATH Keywords: regular category
zbMATH Keywords: pure subobject
zbMATH Keywords: flat object
zbMATH Keywords: regular object
zbMATH Keywords: (dual) purely Rickart object
zbMATH Keywords: (dual) purely Baer object
zbMATH Keywords: (dual) Rickart object
zbMATH Keywords: (dual) Baer object
zbMATH Keywords: module
zbMATH Keywords: comodule
MaRDI profile type: Publication
full work available at URL: s00009-021-01859-6
OpenAlex ID: W3197247052
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DOI: 10.1007/S00009-021-01859-6
description: scientific article; zbMATH DE number 7397614