| Title of paper:
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Intuitionistic L-fuzzy essential and closed submodules
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| Author(s):
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| P. K. Sharma
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| P. G. Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
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| pksharma@davjalandhar.com
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| Kanchan
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| IKG Punjab Technical University, Jalandhar, Punjab, India
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| kanchan4usoh@gmail.com
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| Gagandeep Kaur
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| Department of Applied Science, GNDEC, Ludhiana, Punjab, India
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| loteygagandeepkaur@gmail.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 4, pages 44-54
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| DOI:
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https://doi.org/10.7546/nifs.2021.27.4.44-54
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| Download:
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 PDF (222 Kb, Info)
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| Abstract:
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Let R be a commutative ring with identity and M be an R-module. An intuitionistic L-fuzzy submodule (ILFSM) C of an intuitionistic L-fuzzy module A of R-module M, is called an intuitionistic L-fuzzy essential submodule in A, if C ∩ B ≠ χ{θ} for any non-trivial ILFSM B of A. In this case we say that A is an essential extension of C. Also, if C has no proper essential extension in A, then C is called an intuitionistic L-fuzzy closed submodule in A. Further, for ILFSMs B, C of A, C is called complement of B in A if C is maximal with the property that B ∩ C = χ{θ}. We study these mentioned notations which are generalization of the notions of essential submodule, closed submodule and complement of a submodule in the intuitionistic L-fuzzy module theory. We prove many basic properties of both these concepts.
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| Keywords:
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Intuitionistic L-fuzzy submodule, Intuitionistic L-fuzzy essential submodule, Intuitionistic L-fuzzy closed submodule.
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| AMS Classification:
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03F55, 16D10, 08A72.
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| References:
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- Anderson, F. W., & Fuller, K. R. (1992). Rings and Categories of Modules. Second edition, Springer Verlag.
- Atanassov, K., & Stoeva, S. (1984). Intuitionistic L-fuzzy sets. Cybernetics and System Research, Vol. 2, Elsevier Sci. Publ. Amsterdam, 539–540.
- Birkhoff, G. (1967). Lattice Theory. American Math. Soci. Coll. Publ., Rhode Island.
- Deschrijver, G., & Kerre, E. E. (2003). On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, 133, 227–235.
- Goguen, J. (1967). L-fuzzy sets. Journal of Mathematical Analysis and Applications, 18, 145–174.
- Isaac, P. (2007). Essential L-fuzzy submodules of an L-module. Journal of Fuzzy Mathematics, 15(2), 355–362.
- Kanchan, Sharma, P. K., & Pathania, D. S. (2020). Intuitionistic L-fuzzy submodules. Advances in Fuzzy Sets and Systems, 25(2), 123–142.
- Kasch, F. (1982). Modules and Rings. Academic Press, London.
- Marhon, H. K., & Khalaf, H. Y. (2020). Some Properties of the Essential Fuzzy and Closed Fuzzy Submodules. Iraqi Journal of Science, 61(4), 890–897.
- Meena, K., & Thomas, K. V. (2011). Intuitionistic L-fuzzy Subrings. International Mathematics Forum, 6(52), 2561–2572.
- Palaniappan, N., Naganathan, S., & Arjunan, K. (2009). A study on Intuitionistic L-fuzzy Subgroups. Applied Mathematics Sciences, 3(53), 2619–2624.
- Sharma, P. K., & Kanchan. (2018). On intuitionistic L-fuzzy prime submodules. Annals of Fuzzy Mathematics and Informatics, 16(1), 87–97.
- Sharma, P. K., & Kanchan. (2020). On intuitionistic L-fuzzy primary and P-primary submodules. Malaya Journal of Matematik, 8(4), 1417–1426.
- Wang, G. J., & He, Y. Y. (2000). Intuitionistic fuzzy sets and L-fuzzy sets. Fuzzy Sets and Systems, 110, 271–274.
- Wisbauer, R. (1991). Foundations of Module and Ring Theory. Gordon and Breach, Philadelphia.
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