SavedAdd your journal

Journals / İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi / 2024 / Cilt: 23 Sayı: 46

E-EXACT SEQUENCE AND SOME RESULTS

Abuzer Gündüz(SAKARYA ÜNİVERSİTESİ)0000-0003-3351-2443
Pages
319–328
Publication Date
2024-12-27
🏛️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)

In this note, we present the concept of the characterization of E-homotopy and E-resolution with some results such as chain map for e-exact sequence and comparing theorem for e-exact sequence.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let R be a commutative ring with identity, M be a R-module and N be a submodule of M.
📊
Key Findings & Data:N is called to be essential (large) in M if N∩Rm≠0 for any nonzero element m∈M and we showed by N≤_e M.
💡
Conclusion & Impact:In this note, we present the concept of the characterization of E-homotopy and E-resolution with some results such as chain map for e-exact sequence and comparing theorem for e-exact sequence.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:E-injektif modüller · e-tam diziler · contravariant functor

Abstract

Let R be a commutative ring with identity, M be a R-module and N be a submodule of M. N is called to be essential (large) in M if N∩Rm≠0 for any nonzero element m∈M and we showed by N≤_e M. A sequence of R-modules and R-morphisms …→┴ M_(i-1) □(→┴f_(i-1) M_i →┴f_i ) M_(i+1) →┴f_(i+1) … is called exact at M_i if Im(f_(i-1) )=Ker (f_i). Also this sequence is called e-exact at M_i if Im(f_(i-1))≤_e Ker(f_i) and it is called e-exact if it is e-exact at each M_i. In this note, we present the concept of the characterization of E-homotopy and E-resolution with some results such as chain map for e-exact sequence and comparing theorem for e-exact sequence.

Özet

R birimli ve değişmeli bir halka, M bir R modül ve N, M ‘nin bir alt modülü olsun. Eğer sıfırdan farklı bir m∈M elemanı için N∩Rm≠0 gerçekleniyorsa N’ye M ‘nin bir büyük alt modülü denir ve N≤_e M ile gösterilir. Bir R-modül dizisi için …→┴ M_(i-1) □(→┴f_(i-1) M_i →┴f_i ) M_(i+1) →┴f_(i+1) … her M_i için Im(f_(i-1) )=Ker (f_i) oluyorsa bu diziye tam (exact) dizi denir. Ayrıca her M_i için Im(f_(i-1))≤_e Ker(f_i) oluyorsa bu diziye e-exact dizi denir. Bu çalışmada tam (exact) diziler teorisinin bir genişlemesi olan E-exact diziler teorisi için E-homotopy and E-resolution tanımlanmış ve zincir map ve karşılaştırma teoremi gibi ilgili bir kısım sonuçlar verilmiştir.

🔖

Cite This Article

Gündüz, A. (2024). E-EXACT SEQUENCE AND SOME RESULTS. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi, Cilt: 23 Sayı: 46, 319–328. https://doi.org/10.55071/ticaretfbd.1434248

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (9)

  1. Akray, I., & Zebari, A. (2020). Essential exact sequences. Communications of the Korean Mathematical Society, 35(2), 469-480.
  2. Alizade, R., & Pancar, A. (1999). Homoloji cebire giris. Ondokuz Mayıs Universitesi Yayınları, Samsun.
  3. Anvariyeh, S. M., & Davvaz, B. (2005). On quasi-exact sequences. Bull.Korean Math. Soc., 42(1), 149-155.
  4. Anvariyeh, S. M., & Davvaz, B. (2002). U-Split-Exact Sequences. Far East J. Math Sci. (FJMS), 4, 2, 2009-219.
  5. Davaz, B. (2002). A generalization of homological algebra, J. Korean math. Soc. 39, no. 6, 881-898.
  6. Davaz, B. & Parnian-Garameleky, Y. A. (1999). A note on Exact Sequences, Bull. Malays. Math. Sci. Soc. (2) 22, no. 1, 53-56.
  7. Gunduz, A., & Osama, N. A. J. I. (2022). A Note On E-Injective Modules. Sakarya University Journal of Science, 26(6), 1262-1266.
  8. Hungerford, T. W., & Hungerford, T. W. (1974). Categories. Algebra, 464-484.
  9. Tercan, A., & Yücel, C. C. (2016). Module theory. Extending Modules and Generalizations, Bassel: Birkhäuser–Springer.