Nearly locally hollow modules

Document Type : Research Paper


Department of Mathematics, College of Education for Pure Science, University of Tikrit, Tikrit, Iraq


Let $R$ be a commutative ring with identity and let $M$ be an R-module. This study presents the nearly locally hollow module that's a strong form of a hollow module. We present that an $R$-module $M$ is nearly locally hollow if M has a unique semi-maximal sub-module that contains all small sub-modules of $M$. The current study deals with this class of modules and gives several fundamental properties related to this concept.


[1] M.S. Abbas and F.M. Manhal, d-small submodules and d-small projective modules, Int. J. Algebra 12 (2018) 25–30.
[2] K.M. Ali, Hollow Modules and Semihollow modules, Thesis in College of Science, University of Baghdad, 2005.
[3] Z.T. Khlaif and N.K. Abdullah, L-hollow modules, Tikrit J. Pure Sci. 24 (2019) 104–109.
[4] M.F. Manhal, Essential-Small M-Projective Modules, Thesis College of science, Mustansiriyah University, 2018.
[5] M. Mohammed and A.G. Ahmed, On Some Properties of hollow and hollow dimension modules, Pure Appl. Math. J. 2 (2013) 156–161.
[6] K.I. Nagam, Local lifting module with some of there generalizations, Thesis in Collge of Science, University of Tikrit, 2019.
[7] T. Unsal, ¨ On multiplication modules, Int. Math. Forum 2 (2007) 1415–1420.
[8] Y.K. Hatem, Semimaximal Submodules, M. Sc. Thesis, University of Baghdad, 2007.
[9] Y. Talebi, A.R. Moniri Hamzekolaee, M. Hosseinpour and S. Asgari, A new generalization of t-lifting modules, J. Algebra Related Topics 8 (2020) 1–13.
Volume 13, Issue 1
March 2022
Pages 2293-2301
  • Receive Date: 01 December 2021
  • Revise Date: 21 December 2021
  • Accept Date: 29 December 2021