Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 5

On the locally socle of C(X) whose local cozeroset is cocountable (cofinite)

Pages
1430–1436
Publication Date
2022-10-18
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)

We introduce and study the concept of colocally socle of $C(X)$ as $C_{mu}{S_{lambda}}(X)=left{ fin C(X):|Xbackslash {S}^{lambda}_{f}|

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $C_F(X)$ be the socle of $C(X)$ (i.e., the sum of minimal ideals of $C(X)$).
📊
Key Findings & Data:Let $C_F(X)$ be the socle of $C(X)$ (i.e., the sum of minimal ideals of $C(X)$).
💡
Conclusion & Impact:We introduce and study the concept of colocally socle of $C(X)$ as $C_{mu}{S_{lambda}}(X)=left{ fin C(X):|Xbackslash {S}^{lambda}_{f}|
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Let $C_F(X)$ be the socle of $C(X)$ (i.e., the sum of minimal ideals of $C(X)$). We introduce and study the concept of colocally socle of $C(X)$ as $C_{mu}{S_{lambda}}(X)=left{ fin C(X):|Xbackslash {S}^{lambda}_{f}|

🔖

Cite This Article

Soltanpour, S. (2022). On the locally socle of C(X) whose local cozeroset is cocountable (cofinite). Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1430–1436. https://ajindex.com/articles/529735

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. F. Azarpanah and O.A.S. Karamzadeh, Algebraic characterization of some discon- nected spaces, Italian. J. Pure Appl. Math. 12, 155–168, 2002
  2. F. Azarpanah, O.A.S. Karamzadeh and S. Rahmati, C(X) VS. C(X) modulo its socle, Colloq. Math. 3, 315–336, 2008
  3. T. Dube, Contracting the socle in rings of continuous functions, Rend. Semin. Mat. Univ. Padova, 123, 37–53, 2010
  4. R. Engelking, General topology, Berlin, Germany, Heldermann Verlag, 1989
  5. A.A. Estaji and O.A.S. Karamzadeh, On C(X) modulo its socle, Comm. Algebra. 31, 1561–1571, 2003
  6. M. Ghadermazi, O.A.S. Karamzadeh and M. Namdari, On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova, 129, 47–69, 2013
  7. M. Ghadermazi, O.A.S. Karamzadeh and M. Namdari, C(X) versus its functionally countable subalgebra, to appear in the Bull. Iran. Math. Soc. 2018
  8. S. Ghasmzadeh, O.A.S. Karamzadeh and M. Namdari, The super socle of the ring of continuous functions, Math. Slovaca, 67 (4), 1001–1010, 2017
  9. L. Gillman and M. Jerison, Rings of continuous functions, Springer-Verlag, 1976
  10. K.R. Goodearl, Von Neumann regular rings, Pitman, 1979
  11. S. Mehran and M. Namdari, The -super socle of the ring of continuous function, Categ. Gen. Algebr. Struct. Appl. 6, 1–13, 2017
  12. R. Mehri and R. Mohamadian, On the locally subalgebra of C(X) whose local domain is cocountable, Hacet. J. Math. Stat. 46 (6), 1053-1068, 2017
  13. O.A.S. Karamzadeh and M. Rostami, On the intrinsic topology and some related ideals of C(X), Proc. Amer. Math. Soc. 93, 179–184, 1985
  14. O.A.S. Karamzadeh, M. Namdari and S. Soltanpour, On the locally functionally countable subalgebra of C(X), Appl. Gen. Topol. 16 (2), 183–207, 2015
  15. M. Namdari and S. Soltanpour, Locally socle of C(X), J. Adv. Math. Model. 4 (2), 87–99, 2014.