Abstract
In this paper, first we give the definition of \({\mathcal {F}}\)-copartial morphisms with an additive exact substructure \({\mathcal {F}}\) of an exact structure \({\mathcal {E}}\) in an additive category \({\mathcal {A}}\). Then, we study many properties of \({\mathcal {F}}\)-copartial morphisms. Moreover, we define \({\mathcal {F}}\)-copartial morphisms with a pure-exact structure \({\mathcal {F}}\) and with a finite pure-exact structure \({\mathcal {F}}\) in the category of modules over a ring and call them copartial morphisms and finitely copartial morphisms, respectively. We also investigate the relations between them and give the new characterizations of finitely (singly) pure-projective modules, flat modules and finitely (singly) projective modules with copartial morphisms and finitely copartial morphisms. Finally, we define \(\mu \)-partial morphisms for a defining matrix \(\mu \) and give a new characterization of semi-compact modules with \(\mu \)-partial morphisms.
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Kalebog̃az, B. \({\mathcal {F}}\)-Copartial Morphisms. Bull. Malays. Math. Sci. Soc. 46, 32 (2023). https://doi.org/10.1007/s40840-022-01407-9
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DOI: https://doi.org/10.1007/s40840-022-01407-9