I-prime fuzzy submodules

Sagban, Manal Ali; Zyarah, Ali Abd Alhussein; Hussain, Ahmed Hadi

doi:10.47974/JDMSC-1563

Open Access Research Article

I-prime fuzzy submodules

^*Manal Ali SagbanCorresponding authormnally061@gmail.comGeneral Directorate of Education for the Holy Karbala, Iraqi Ministry of EducationKarbala, IraqView full profile → , Ali Abd Alhussein Zyarahaliziara107@gmail.comGeneral Directorate of Education for the Holy Karbala, Iraqi Ministry of EducationKarbala, IraqView full profile → , Ahmed Hadi Hussainmet.ahmed.hadi@uobabylon.edu.iqDepartment of Automobile EngineeringCollege of Engineering Al-MusayabUniversity of BabylonBabil, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1169–1174Vol. 26Issue 4June 2023DOI: 10.47974/JDMSC-1563 Crossmark XML

Received:: 02 Feb 2022
Accepted:: 02 Mar 2022
Published Online:: 15 Jul 2023
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1563
Pages:: 1169–1174

Abstract

In this paper, we introduce a new generalization of prime F.S.M (P.F.S), called I- prime F.S.M and I be any ideal of a commutative ring R also, we study some properties of it and giving some characterizations of I-P.F.S. We establish the situation of I-P.F.Ss in F.M of the R-module and, we show that I-P.F.S and P.F.S are coincident under certain conditions.

Keywords

Prime fuzzy submodule Weakly prime fuzzy submodule and I-prime submodule

Subject Classifications

03B5203E7208A72

References

[1] Zadeh, L.A., Fuzzy sets, in Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A Zadeh. World Scientific. p. 394-432 (1996).
[2] Malik, A. and J.N. Mordeson, Fuzzy prime ideals of a ring. Fuzzy Sets and Systems, 37(1), p. 93-98 (1990).
[3] Rabi, H., Prime F.S.Ms and Prime F.Ms., M. Sc. Thesis, University of Baghdad (2001).
[4] Akray, I. and H.S. Hussein, I-prime submodules. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 33(2), p. 165-173 (2017).
[5] Zyarah, A.A.A. and N.S. Al-Mothafar, On primary radical RΓ-submodules of RΓ-modules. Journal of Discrete Mathematical Sciences and Cryptography, 23(5), p. 1001-1007 (2020).
[6] Shahad, H.A., and N.S. Al-Muthafar, On essential-prime sub-modules. Journal of Discrete Mathematical Sciences and Cryptography, 24(7), p. 1973-1977 (2021).
[7] Rosenfeld, A., Fuzzy groups. Journal of Mathematical Analysis and Applications, 35(3): p. 512-517 (1971).
[8] Kumar, R., Fuzzy semiprimary ideals of rings. Fuzzy Sets and Systems, 42(2), p. 263-272 (1991).
[9] Zahedi, M., Some results on L-F.Ms. Fuzzy Sets and Systems, 55(3),
p. 355-361 (1993).
[10] Abou-Draeb, A., B. Al-Zreegawi, and Y.K. Al-Duja, Prime F.S.Ms and Strongly Prime F.S.Ms Over Near-ring. Journal of Babylon Univ. Pure and Applied Science, 22(3), p. 984-996 (2014).
[11] Mahjoob, R. and S. Qiami. On Weakly Prime F.S.Ms. in The 46th Annual Iranian Mathematics Conference (2015).
[12] Zyarah, A.A.A. and A.K.H. Alghafil, General formula for a particular solution to the ordinary differential equation by variation of parameters of k th order. Journal of Interdisciplinary Mathematics, p. 1-6 (2021).

Views: 145Downloads: 63Citations: 0