Almost maximal, e-maximal and e-simple fuzzy submodules

Document Type : Research Paper


Department of Mathematics, College of Education for Pure Sciences, Ibn-Al-Haitham, University of Baghdad, Iraq


In this paper, the concepts of almost maximal submodules are fuzzified and studied. Also, three new concepts are introduced, which are: e-simple submodules, Ee-simple modules and e-maximal submodules. Then these concepts are fuzzified and studied.


[1] M.S. Abaas, On fully stable moduls, Ph. D. Thesis, University of Baghdad, 1990.
[2] I.M.A. Hadi, On fuzzy ideals of fuzzy rings, Math. Phys. 16 (2001) 1–4.
[3] A.H. Ghaleb, Generalization of Regular Modules and Pure Submodules, Ph.D. Thesis, University of Baghdad,
[4] K.M. Hassan and Y.K. Hatem, Some properties of the essential fuzzy and closed fuzzy submodules, Iraqi J. Sci.
61 (2020) 890–897.
[5] K.R. Goodreal, Ring Theory Non Singular Rings and Modules, Marci-Dekker, New York and Basel, 1976.
[6] M.A. Inaam and K. Ali, On almost maximal submodules, College Educ. J. Al Mustansiriya Univ. 26 (2008)
[7] L. Martinez, Fuzzy modules over fuzzy rings in connection with fuzzy ideal of ring, J. Fuzzy Math. 4 (1996)
[8] M. Mashinchi and M.M. Zahedi, On L-fuzzy primary submodules, Fuzzy Sets Syst. 49 (1992) 231–236.
[9] A.H. Maysoun, F-regular fuzzy modules, M. Sc. Thesis, University of Baghdad, 2002.
[10] A.H. Maysoun, Fuzzy T-maximal submodules and fuzzy semimaximal submodules, Ph. D. Thesis, University of
Baghdad, 2021.
[11] H. J. Rabi, Prime fuzzy submodule and prime fuzzy modules, M. Sc. Thesis, University of Baghdad, 2001.
[12] L.A. Zadeh, Fuzzy sets, Info. Cont. 8 (1965) 338–353.
Volume 13, Issue 1
March 2022
Pages 103-113
  • Receive Date: 09 March 2021
  • Revise Date: 18 April 2021
  • Accept Date: 04 May 2021