SavedAdd your journal

Journals / Journal of Algebra Combinatorics Discrete Structures and Applications / 2019 / Cilt: 6 - Sayı: 2

Coretractable modules relative to a submodule

Ali Reza Moniri HAMZEKOLAEE
Yahya TALEBİ
Pages
95–103
Publication Date
2019-05-07
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 also provide some examples to illustrate special cases.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $R$ be a ring and $M$ a right $R$-module.
📊
Key Findings & Data:Let $N$ be a proper submodule of $M$.
💡
Conclusion & Impact:We also provide some examples to illustrate special cases.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Coretractable module · N-coretractable module

Abstract

Let $R$ be a ring and $M$ a right $R$-module. Let $N$ be a proper submodule of $M$. We say that $M$ is $N$-coretractable (or $M$ is coretractable relative to $N$) provided that, for every proper submodule $K$ of $M$ containing $N$, there is a nonzero homomorphism $f:M/K\rightarrow M$. We present some conditions that a module $M$ is coretractable if and only if $M$ is coretractable relative to a submodule $N$. We also provide some examples to illustrate special cases.

🔖

Cite This Article

HAMZEKOLAEE, A. R. M., TALEBİ, Y. (2019). Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 6 - Sayı: 2, 95–103. https://ajindex.com/articles/861535

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. A. N. Abyzov, A. A. Tuganbaev, Retractable and coretractable modules, J. Math. Sci. 213(2) (2016) 132–142
  2. B. Amini, M. Ershad, H. Sharif, Coretractable modules, J. Aust. Math. Soc. 86(3) (2009) 289–304
  3. F. W. Anderson, K. R. Fuller, Rings and Categories of Modules, Springer-Verlog, New York, 1992
  4. N. O. Ertas, D. K. Tütüncü, R. Tribak, A variation of coretractable modules, Bull. Malays. Math. Sci. Soc. 41(3) (2018) 1275–1291
  5. S. M. Khuri, Endomorphism rings and lattice isomorphisms, J. Algebra 56(2) (1979) 401–408
  6. S. M. Khuri, Nonsingular retractable modules and their endomorphism rings, Bull. Aust. Math. Soc. 43(1) (1991) 63–71
  7. T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York, 1999
  8. G. Lee, S. T. Rizvi, C. S. Roman, Dual Rickart modules, Comm. Algebra 39(11) (2011) 4036-4058
  9. S. H. Mohamed, B. J. Müller, Continuous and Discrete Modules, London Math. Soc. Lecture Notes Series 147, Cambridge, University Press, Cambridge, 1990
  10. A. R. M. Hamzekolaee, A generalization of coretractable modules, J. Algebraic Syst. 5(2) (2017) 163–176
  11. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991
  12. J. M. Zelmanowitz, Correspondences of closed submodules, Proc. Amer. Math. Soc. 124(10) (1996) 2955–2960
  13. J. Žemlicka, Completely coretractable rings, Bull. Iranian Math. 39(3) (2013) 523–528
  14. Z. Zhengping, A lattice isomorphism theorem for nonsingular retractable modules, Canad. Math. Bull. 37(1) (1994) 140–144
  15. Y. Zhou, Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq. 7(3) (2000) 305–318.