SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2022 / Cilt: 71 Sayı: 4

On $\mathcal{F}$-cosmall morphisms

Berke KALEBOĞAZ
Derya KESKİN TÜTÜNCÜ
Pages
968–977
Publication Date
2022-12-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

As an application, we investigate our results in a pure-exact substructure $\mathcal{F}$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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 $\mathcal{A}$.
📊
Key Findings & Data:We show that every $\mathcal{F}$-cosmall quotient is right minimal in some cases.
💡
Conclusion & Impact:As an application, we investigate our results in a pure-exact substructure $\mathcal{F}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$\mathcal{F}$-cosmall quotients · right minimal morphisms · $\mathcal{F}$-superfluous quotients

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 $\mathcal{F}$.

🔖

Cite This Article

KALEBOĞAZ, B., TÜTÜNCÜ, D. K. (2022). On $\mathcal{F}$-cosmall morphisms. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 71 Sayı: 4, 968–977. https://ajindex.com/articles/903591

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (9)

  1. 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.
  2. Bühler, T., Exact categories, Expo. Math., 28(1) (2010), 1–69.
  3. 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
  4. 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
  5. Fieldhouse, D. J., Pure theories, Math. Ann., 184 (1969), 1-18.
  6. 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.
  7. 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.
  8. 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
  9. Ziegler, M., Model theory of modules, Annals Pure Appl. Logic, 26 (1984), 149-213.