ASPG Menu
search

American Scientific Publishing Group

verified Journal

International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

Publication Model

Open access · Articles freely available online · APC applies after acceptance

Submit Manuscript send
International Journal of Neutrosophic Science
Full Length Article

Volume 22 • Issue 3 • PP: 36-52 • 2023

On Radical of Neutrosophic Primary Submodule

M. Vasuki 1*
mail
,
P. Senthil Kumar 1
mail
,
Said Broumi 2
mail
,
N. Rajesh 1
mail
1Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur-613005, Tamilnadu, India
2Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.220303
format_quote Cite this article
Received: April 26, 2023 Revised: July 08, 2023 Accepted: October 04, 2023
PDF Icon View PDF open_in_new

Abstract

In this paper, we introduce and study the concept of neutrosophic submodules and neutrosophic primary submodule with the help of the definition of a radical submodule, and we also study the properties of these submodules. Furthermore, homomorphic image and preimage of neutrosophic primary submodule are investigated.

Keywords

neutrosophic submodules radical submodule neutrosophic primary submodule.

References

[1] J. M. Abulebda Lamis, Uniformly primal submodule over noncommutative ring, Journal of Mathematics, vol. 2020, Article ID 1593253, 4 pages, 2020.

[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 197, 1986.

[3] M. Behboodi and H. Koohy, Weakly prime modules, Vietnam Journal of Mathematics, 32 (2) (2004), 185-195.

[4] B. Davvaz, W. A. Dudek, and Y. B. Jun, Intuitionistic fuzzy submodules, Information Sciences, 176 (3) (2006), 285-300.

[5] R. Biswas, Intuitionistic fuzzy subgroups, Mathematical Forum, 10 (1989), 37-46.

[6] J. Goswami and H. K. Saikia, On the spectrum of weakly prime submodule, Thai Journal of Mathematics, 19 (1) (2019), 51-58.

[7] K. Hur, S.Y. Jang, and H.W. Kang, Intuitionistic fuzzy ideals of a ring, The Pure and Applied Mathematics, 12 (3) (2005), 193-209.

[8] K. Hur, S.Y. Jang, and H.W. Kang, Intuitionistic fuzzy subgroupoids, International Journal of Fuzzy Logic and Intelligent Systems, 3 (1) (2003), 72-77.

[9] A. Iampan, S. R. Vidhya and N. Rajesh, Polynomial ideals of a ring based on neutrosophic sets (under preparation).

[10] D. S. Lee and C. H. Park, On intuitionistic fuzzy w-primary submodules, Honam Mathematical Journal, 29 (4) (2007), 631-640.

[11] M. Mashinchi and M. M. Zahedi, On L-fuzzy primary submodules, Fuzzy Sets and Systems, 49 (2) (1992), 231-236.

[12] C. V. Negoita and D. A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Springer, Berlin, Germany, 1975.

[13] N. D. H. Nghiem, S. Baupradist, and R. Chinram, On nearly prime submodules of unitary modules, Journal of Mathematics, vol. 2018, pp. 1-4, 2018.

[14] S. Rahman and H. K. Saikia, Some aspects of Atanassov’s intuitionistic fuzzy submodule, International Journal of Pure and Applied Mathematics, 77 (2012), 369-383.

[15] A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications, 35 (1971), 512–517.

[16] P. Sharma, Translates of intuitionistic fuzzy subring, International Review of Fuzzy Mathematics, 6 (2011), 77-84.

[17] P. K. Sharma and K. Gagandeep, Residual quotient and annihilator of intuitionistic fuzzy sets of ring and module, International Journal of Computer Science and Information Technology, 9 (2017), 1-15.

[18] P. K. Sharma and G. Kaur, Intuitionistic fuzzy prime spectrum of a ring, International Journal of Fuzzy Systems, 9 (2017), 167–175.

[19] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24(3) (2005), 287-297.

[20] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (3) (1965), 338-353.

 

Cite This Article

Choose your preferred format

format_quote
Vasuki, M., Kumar, P. Senthil, Broumi, Said, Rajesh, N.. "On Radical of Neutrosophic Primary Submodule." International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 3, 2023, pp. 36-52. DOI: https://doi.org/10.54216/IJNS.220303
Vasuki, M., Kumar, P., Broumi, S., Rajesh, N. (2023). On Radical of Neutrosophic Primary Submodule. International Journal of Neutrosophic Science, Volume 22(Issue 3), 36-52. DOI: https://doi.org/10.54216/IJNS.220303
Vasuki, M., Kumar, P. Senthil, Broumi, Said, Rajesh, N.. "On Radical of Neutrosophic Primary Submodule." International Journal of Neutrosophic Science Volume 22, no. Issue 3 (2023): 36-52. DOI: https://doi.org/10.54216/IJNS.220303
Vasuki, M., Kumar, P., Broumi, S., Rajesh, N. (2023) 'On Radical of Neutrosophic Primary Submodule', International Journal of Neutrosophic Science, Volume 22(Issue 3), pp. 36-52. DOI: https://doi.org/10.54216/IJNS.220303
Vasuki M, Kumar P, Broumi S, Rajesh N. On Radical of Neutrosophic Primary Submodule. International Journal of Neutrosophic Science. 2023;Volume 22(Issue 3):36-52. DOI: https://doi.org/10.54216/IJNS.220303
M. Vasuki, P. Kumar, S. Broumi, N. Rajesh, "On Radical of Neutrosophic Primary Submodule," International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 3, pp. 36-52, 2023. DOI: https://doi.org/10.54216/IJNS.220303
Digital Archive Ready