On $\mathcal{F}$-cosmall morphisms

Year 2022, Volume: 71 Issue: 4, 968 - 977, 30.12.2022

Berke Kaleboğaz Derya Keskin Tütüncü

https://doi.org/10.31801/cfsuasmas.1061084

Cited By: 1

Abstract

In this paper, we first define the notion of $\mathcal{F}$-cosmall quotient for an additive exact substructure $\mathcal{F}$ of an exact structure $\mathcal{E}$ in an additive category $\mathcal{A}$. We show that every $\mathcal{F}$-cosmall quotient is right minimal in some cases. We also give the definition of $\mathcal{F}$-superfluous quotient and we relate it the approximation of modules. As an application, we investigate our results in a pure-exact substructure $\mathcal{F}$.

Keywords

$\mathcal{F}$-cosmall quotients, right minimal morphisms, $\mathcal{F}$-superfluous quotients

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