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Coretractable modules relative to a submodule

Year 2019, , 95 - 103, 07.05.2019
https://doi.org/10.13069/jacodesmath.561322

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.

References

  • [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.
Year 2019, , 95 - 103, 07.05.2019
https://doi.org/10.13069/jacodesmath.561322

Abstract

References

  • [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.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ali Reza Moniri Hamzekolaee 0000-0002-2852-7870

Yahya Talebi 0000-0003-2311-4628

Publication Date May 7, 2019
Published in Issue Year 2019

Cite

APA Hamzekolaee, A. R. M., & Talebi, Y. (2019). Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications, 6(2), 95-103. https://doi.org/10.13069/jacodesmath.561322
AMA Hamzekolaee ARM, Talebi Y. Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications. May 2019;6(2):95-103. doi:10.13069/jacodesmath.561322
Chicago Hamzekolaee, Ali Reza Moniri, and Yahya Talebi. “Coretractable Modules Relative to a Submodule”. Journal of Algebra Combinatorics Discrete Structures and Applications 6, no. 2 (May 2019): 95-103. https://doi.org/10.13069/jacodesmath.561322.
EndNote Hamzekolaee ARM, Talebi Y (May 1, 2019) Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications 6 2 95–103.
IEEE A. R. M. Hamzekolaee and Y. Talebi, “Coretractable modules relative to a submodule”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 6, no. 2, pp. 95–103, 2019, doi: 10.13069/jacodesmath.561322.
ISNAD Hamzekolaee, Ali Reza Moniri - Talebi, 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.
JAMA Hamzekolaee ARM, Talebi Y. Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019;6:95–103.
MLA Hamzekolaee, Ali Reza Moniri and Yahya Talebi. “Coretractable Modules Relative to a Submodule”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 6, no. 2, 2019, pp. 95-103, doi:10.13069/jacodesmath.561322.
Vancouver Hamzekolaee ARM, Talebi Y. Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019;6(2):95-103.