| 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, File 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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