Vassia Atanassova at 08:24, 22 December 2021

2021-12-22T08:24:18Z

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	{{issue/author		{{issue/author
	\| author = P. K. Sharma		\| author = P. K. Sharma
	\| institution = P.G. ~~department~~ of Mathematics, D.A.V. College		\| institution = P. G. Department of Mathematics, D.A.V. College
	\| address = Jalandhar, Punjab, India		\| address = Jalandhar, Punjab, India
	\| email-before-at = pksharma		\| email-before-at = pksharma

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2021-12-21T16:28:38Z

Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}}..."

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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
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[[Category:Publications in 2021 year|{{PAGENAME}}]]
{{issue/title
| title = Intuitionistic ''L''-fuzzy essential and closed submodules
| shortcut = nifs/27/4/44-54
}}
{{issue/author
| author = P. K. Sharma
| institution = P.G. department of Mathematics, D.A.V. College
| address = Jalandhar, Punjab, India
| email-before-at = pksharma
| email-after-at = davjalandhar.com
}}
{{issue/author
| author = Kanchan
| institution = IKG Punjab Technical University
| address = Jalandhar, Punjab, India
| email-before-at = kanchan4usoh
| email-after-at = gmail.com
}}
{{issue/author
| author = Gagandeep Kaur
| institution = Department of Applied Science, GNDEC
| address = Ludhiana, Punjab, India
| email-before-at = loteygagandeepkaur
| email-after-at = gmail.com
}}
{{issue/data
| issue = [[Notes on Intuitionistic Fuzzy Sets/27/4|Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 4]], pages 44-54
| doi = https://doi.org/10.7546/nifs.2021.27.4.44-54
| file = NIFS-27-4-44-54.pdf
| format = PDF
| size = 222
| abstract = 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''<sub>{''θ''}</sub> 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''<sub>{''θ''}</sub>. 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.

| keywords = Intuitionistic ''L''-fuzzy submodule, Intuitionistic ''L''-fuzzy essential submodule, Intuitionistic ''L''-fuzzy closed submodule.
| ams = 03F55, 16D10, 08A72.
| references =
# 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.
| citations =
| see-also =
}}

Issue:Intuitionistic L-fuzzy essential and closed submodules - Revision history

Vassia Atanassova at 08:24, 22 December 2021

Vassia Atanassova: Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}}..."