Coretractable modules relative to a submodule

Yıl 2019, Cilt: 6 Sayı: 2, 95 - 103, 07.05.2019

Ali Reza Moniri Hamzekolaee Yahya Talebi

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.

Anahtar Kelimeler

Coretractable module, N-coretractable module

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.