Abstract
In this paper, (dual) purely Rickart objects are introduced as generalizations of (dual) Rickart objects in Grothendieck categories. Examples showing the relations between (dual) relative Rickart objects and (dual) relative purely Rickart objects are given. It is shown that in a spectral category, (dual) relative purely Rickart objects coincide with (dual) relative Rickart objects. (Co)products of (dual) relative purely Rickart objects are studied. Classes all of whose objects are (dual) relative purely Rickart are identified. It is shown how this theory may be employed to study (dual) relative purely Baer objects in Grothendieck categories. Also applications to module and comodule categories are given.
| Original language | English |
|---|---|
| Article number | 216 |
| Journal | Mediterranean Journal of Mathematics |
| Volume | 18 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Oct 2021 |
Keywords
- (dual) Baer object
- (dual) Rickart object
- (dual) purely Baer object
- (dual) purely Rickart object
- Abelian category
- Grothendieck category
- comodule
- flat object
- module
- pure subobject
- regular category
- regular object
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