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Coretractable modules relative to a submodule

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

Öz

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.

Kaynakça

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

Öz

Kaynakça

  • [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.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Ali Reza Moniri Hamzekolaee 0000-0002-2852-7870

Yahya Talebi 0000-0003-2311-4628

Yayımlanma Tarihi 7 Mayıs 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

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. Mayıs 2019;6(2):95-103. doi:10.13069/jacodesmath.561322
Chicago Hamzekolaee, Ali Reza Moniri, ve Yahya Talebi. “Coretractable Modules Relative to a Submodule”. Journal of Algebra Combinatorics Discrete Structures and Applications 6, sy. 2 (Mayıs 2019): 95-103. https://doi.org/10.13069/jacodesmath.561322.
EndNote Hamzekolaee ARM, Talebi Y (01 Mayıs 2019) Coretractable modules relative to a submodule. Journal of Algebra Combinatorics Discrete Structures and Applications 6 2 95–103.
IEEE A. R. M. Hamzekolaee ve Y. Talebi, “Coretractable modules relative to a submodule”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 6, sy. 2, ss. 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 (Mayıs 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 ve Yahya Talebi. “Coretractable Modules Relative to a Submodule”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 6, sy. 2, 2019, ss. 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.