Volume 5 • Issue 1 • PP: 08–13 • 2025
LS-Extending Fuzzy Modules
Open Access & Copyright
© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Abstract
The main aim of this paper is extend the notion of S-extending fz-modules into LS-extending fz-modules and study this new notion. This lead us introduce and study other notions such as: purely semisimple, purely extending and purely y-extending fz-modules. Moreover, the relationships LS-extending fz-module with the various types.
Keywords
References
[1] H. H. Abbas and S. N. Al-aeashi, “A fuzzy semiessentialsubmodule of a fuzzy module,” J. of Kufa forMath. and Compute, vol. 1, no. 5, pp. 31–37, 2012.
[2] M. A. Ahmed, M. R. Abbas, and N. R. Adeeb, “Almostsemi-extending modules,” Iraqi Journal of Science,vol. 63, no. 7, pp. 3111–3119, 2022.
[3] M. A. Ahmed, M. R. Abbas, and N. R. Adeeb, “Semiextendingmodules,” International J. of Advanced Scientificand Technical Research, vol. 6, no. 5, pp. 36–46, 2015.
[4] B. H. Al-Bahraany, “Modules with the pure intersection property,” Ph.D. dissertation, College of Science, University of Baghdad, 2000.
[5] B. H. Al-Bahraany, “On purely y-extending modules,” Iraq J. of Sci., vol. 54, no. 3, pp. 672–675, 2013.
[6] M. O. Behboodi, A. S. Karamzadeh, and H. Koohy, “Modules whose certain submodules are prime,” Vietnam Journal of Math., vol. 32, no. 3, pp. 303–317, 2004.
[7] S. Baupradist, B. Chemat, and R. Chinram, “The properties of uniform fuzzy modules and semi-uniform fuzzy modules,” Journal of the Indonesian Mathematical Society, vol. 28, no. 2, pp. 133–146, 2022.
[8] K. Goodearl, Ring Theory, Nonsingular Rings and Modules. New York: Marcel Dekker, 1976.
[9] R. H. Jari, “Prime fuzzy submodules and prime fuzzy modules,” Master’s thesis, University of Baghdad, 2001.
[10] I. M. A. Hadi and M. A. Hamel, “Cancellation and weakly cancellation fuzzy modules,” J. of Basrah Researches, vol. 37, no. 4, 2011.
[11] M. A. Hami, “Fuzzy regular f-modules,” Master’s thesis, University of Baghdad, 2002.
[12] R. Kumar, “Fuzzy semi-primary ideals of rings,” Fuzzy Sets and Systems, vol. 42, pp. 263–272, 1991.
[13] H. K. Marhoon, “Fuzzy closed submodules and fuzzy w-closed submodules with some of their generalization,” Ph.D. dissertation, University of Baghdad, 2020.
[7] S. Baupradist, B. Chemat, and R. Chinram, “The properties of uniform fuzzy modules and semi-uniform fuzzy modules,” Journal of the Indonesian Mathematical Society, vol. 28, no. 2, pp. 133–146, 2022.
[8] K. Goodearl, Ring Theory, Nonsingular Rings and Modules. New York: Marcel Dekker, 1976.
[9] R. H. Jari, “Prime fuzzy submodules and prime fuzzy modules,” Master’s thesis, University of Baghdad, 2001.
[10] I. M. A. Hadi and M. A. Hamel, “Cancellation and weakly cancellation fuzzy modules,” J. of Basrah Researches, vol. 37, no. 4, 2011.
[11] M. A. Hami, “Fuzzy regular f-modules,” Master’s thesis, University of Baghdad, 2002.
[12] R. Kumar, “Fuzzy semi-primary ideals of rings,” Fuzzy Sets and Systems, vol. 42, pp. 263–272, 1991.
[13] H. K. Marhoon, “Fuzzy closed submodules and fuzzy w-closed submodules with some of their generalization,” Ph.D. dissertation, University of Baghdad, 2020.
[14] H. K. Marhoon and M. A. Hamel, “Fuzzy topological modules,” Journal of Mathematical Sciences, vol. 45, no. 3, pp. 215–225, 2022.
[15] S. K. Nimbhorkar and J. A. Khubchandani, “Fuzzy semi-essential submodules and fuzzy semi-closed submodules,” TWMS Journal of Applied and Engineering Mathematics, vol. 13, no. 2, pp. 568–575, 2023.
[16] L. Martinez, “Fuzzy module over fuzzy rings in connection with fuzzy ideals of rings,” J. Fuzzy Math., vol. 4, pp. 843–857, 1996.
[17] A. A. Qaid, “Some results on fuzzy modules,” Master’s thesis, University of Baghdad, 1991.
[18] S. B. Semeen, “Chained fuzzy modules,” Ibn Al- Haitham J. for Pure and Appl. Sci., vol. 23, no. 2, 2010.
[19] F. D. Shyaa, “A study of modules related with tsemisimple modules,” Ph.D. dissertation, College of Science, University of Baghdad, 2018.
[20] Z. Yue, “Prime l-fuzzy ideals and primary l-fuzzy ideals,” Fuzzy Sets and Systems, vol. 27, pp. 345–350, 1988.
[21] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338–353, 1965.
[22] M. M. Zahedi, “On l-fuzzy residual quotient module and p. primary submodule,” Fuzzy Sets and Systems, vol. 51, pp. 333–344, 1992.modules,” Journal of Mathematical Sciences, vol. 45, no. 3, pp. 215–225, 2022.
[15] S. K. Nimbhorkar and J. A. Khubchandani, “Fuzzy semi-essential submodules and fuzzy semi-closed submodules,” TWMS Journal of Applied and Engineering Mathematics, vol. 13, no. 2, pp. 568–575, 2023.
[16] L. Martinez, “Fuzzy module over fuzzy rings in connection with fuzzy ideals of rings,” J. Fuzzy Math., vol. 4, pp. 843–857, 1996.
[17] A. A. Qaid, “Some results on fuzzy modules,” Master’s thesis, University of Baghdad, 1991.
[18] S. B. Semeen, “Chained fuzzy modules,” Ibn Al- Haitham J. for Pure and Appl. Sci., vol. 23, no. 2, 2010.
[19] F. D. Shyaa, “A study of modules related with tsemisimple modules,” Ph.D. dissertation, College of Science, University of Baghdad, 2018.
[20] Z. Yue, “Prime l-fuzzy ideals and primary l-fuzzy ideals,” Fuzzy Sets and Systems, vol. 27, pp. 345–350, 1988.
[21] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338–353, 1965.
[22] M. M. Zahedi, “On l-fuzzy residual quotient module and p. primary submodule,” Fuzzy Sets and Systems, vol. 51, pp. 333–344, 1992.
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