Year 2019, Volume 6 , Issue 2, Pages 95 - 103 2019-05-07

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.
Coretractable module, N-coretractable module
  • [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.
Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0002-2852-7870
Author: Ali Reza Moniri HAMZEKOLAEE (Primary Author)

Orcid: 0000-0003-2311-4628
Author: Yahya TALEBİ

Dates

Publication Date : May 7, 2019

Bibtex @research article { jacodesmath561322, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2019}, volume = {6}, pages = {95 - 103}, doi = {10.13069/jacodesmath.561322}, title = {Coretractable modules relative to a submodule}, key = {cite}, author = {Hamzekolaee, Ali Reza Moniri and Talebi̇, Yahya} }
APA Hamzekolaee, A , Talebi̇, Y . (2019). Coretractable modules relative to a submodule . Journal of Algebra Combinatorics Discrete Structures and Applications , 6 (2) , 95-103 . DOI: 10.13069/jacodesmath.561322
MLA Hamzekolaee, A , Talebi̇, Y . "Coretractable modules relative to a submodule" . Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 95-103 <https://dergipark.org.tr/en/pub/jacodesmath/issue/45030/561322>
Chicago Hamzekolaee, A , Talebi̇, Y . "Coretractable modules relative to a submodule". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 95-103
RIS TY - JOUR T1 - Coretractable modules relative to a submodule AU - Ali Reza Moniri Hamzekolaee , Yahya Talebi̇ Y1 - 2019 PY - 2019 N1 - doi: 10.13069/jacodesmath.561322 DO - 10.13069/jacodesmath.561322 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 95 EP - 103 VL - 6 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.561322 UR - https://doi.org/10.13069/jacodesmath.561322 Y2 - 2019 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Coretractable modules relative to a submodule %A Ali Reza Moniri Hamzekolaee , Yahya Talebi̇ %T Coretractable modules relative to a submodule %D 2019 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 6 %N 2 %R doi: 10.13069/jacodesmath.561322 %U 10.13069/jacodesmath.561322
ISNAD Hamzekolaee, Ali Reza Moniri , Talebi̇, Yahya . "Coretractable modules relative to a submodule". Journal of Algebra Combinatorics Discrete Structures and Applications 6 / 2 (May 2019): 95-103 . https://doi.org/10.13069/jacodesmath.561322
AMA Hamzekolaee A , Talebi̇ Y . Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(2): 95-103.
Vancouver Hamzekolaee A , Talebi̇ Y . Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(2): 95-103.