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Purely Rickart and Dual Purely Rickart Objects in Grothendieck Categories

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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.

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Acknowledgements

The authors would like to thank the referee for her/his guiding and instructive report, which sheds light on this study and enables the dimensions of the work to enlarge.

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  1. Department of Mathematics, Hacettepe University, Beytepe, 06800, Ankara, Turkey

    Sultan Eylem Toksoy

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  1. Sultan Eylem Toksoy
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Correspondence to Sultan Eylem Toksoy.

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Toksoy, S.E. Purely Rickart and Dual Purely Rickart Objects in Grothendieck Categories. Mediterr. J. Math. 18, 216 (2021). https://doi.org/10.1007/s00009-021-01859-6

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  • DOI: https://doi.org/10.1007/s00009-021-01859-6

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