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

References

• Auslander, M., Rieten, I., Smalø S.O., Represantation Theory of Artin Algebras Volume 36 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1995.
• Bühler, T., Exact categories, Expo. Math., 28(1) (2010), 1–69.
• Cortes-Izurdiaga, M., Guil Asensio, P.A., Keskin Tütüncü D., Srivastava, A.K., Endomorphism rings via minimal morphisms, Mediterr. J. Math., 18(152) (2021), 16 pages. https://doi.org/10.1007/s00009-021-01802-9
• Cortes-Izurdiaga, M., Guil Asensio, P.A., Kaleboğaz, B., Srivastava, A.K., Ziegler partial morphisms in additive exact categories, Bull. Math. Sci., 10(3) 2050012 (2020), 37 pages. https://doi.org/10.1142/S1664360720500125
• Fieldhouse, D. J., Pure theories, Math. Ann., 184 (1969), 1-18.
• Kaleboğaz, B., F-copartial morphisms, Accepted in Bull. Malaysian Math. Sci. Soc.
• Keller, B., Chain complexes and stable categories, Manuscripta Math., 67(4) (1990), 379–417.
• Keskin Tütüncü, D., Subrings of endomorphism rings associated with right minimal morphisms, submitted.
• Monari Martinez, E., On Pure-Injective Modules, Abelian Groups and Modules, Proceedings of the Udine Conference CISM Courses and Lectures No. 287, Springer-Verlag, Vienna-New York (1984), 383-393. https://doi.org/10.1007/978-3-7091-2814-5 29
• Warfield, R. B., Purity and algebraic compactness for modules, Pacific J. Math., 28 (1969), 699–719.
• Zhu, H.Y., Ding N. Q., S-superfluous and S-essential homomorphisms, Acta Math. Sci., 29B(2) (2009), 391-401. https://doi.org/10.1016/S0252-9602(09)60038-2
• Ziegler, M., Model theory of modules, Annals Pure Appl. Logic, 26 (1984), 149-213.