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Communications in Algebra Volume 46, 2018 - Issue 10
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Original Articles

Strongly Rickart objects in abelian categories

Septimiu CriveiFaculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, RomaniaCorrespondence[email protected]
ORCID Iconhttp://orcid.org/0000-0001-6382-9148
ORCID Icon &
Gabriela OlteanuDepartment of Statistics-Forecasts-Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania
Pages 4326-4343 | Received 24 Sep 2017, Published online: 08 Mar 2018
 
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ABSTRACT

We introduce and study (dual) strongly relative Rickart objects in abelian categories. We prove general properties, we analyze the behaviour with respect to (co)products, and we study the transfer via functors. We also give applications to Grothendieck categories, (graded) module categories and comodule categories. Our theory of (dual) strongly relative Rickart objects may be employed in order to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian categories.

2000 MATHEMATICS SUBJECT CLASSIFICATION:

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