Intuitionistic fuzzification of essential submodule with respect to an arbitrary submodule
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let $R$ be a commutative ring and $B$ be an intuitionistic fuzzy submodule (IFSM) of an $R$-module $M$. Then an IFSM $A$ of $M$ is called $B$-essential in $M$ provided for each IFSM $C$ of $M$, $A \cap C \subseteq B$ implies that $C \subseteq B$. Further, for IFSMs $A, B, C$ of $M$, the IFSM $C$ is called $B$-complement to $A$ if $C$ is maximal with respect to the property that $A\cap C \subseteq B$. We study these mentioned notations which are generalization of the intuitionistic fuzzy essential (compliment) submodules, introduced by Basnet in [5]. Here we shall study some related results.
Abstract
Let $R$ be a commutative ring and $B$ be an intuitionistic fuzzy submodule (IFSM) of an $R$-module $M$. Then an IFSM $A$ of $M$ is called $B$-essential in $M$ provided for each IFSM $C$ of $M$, $A \cap C \subseteq B$ implies that $C \subseteq B$. Further, for IFSMs $A, B, C$ of $M$, the IFSM $C$ is called $B$-complement to $A$ if $C$ is maximal with respect to the property that $A\cap C \subseteq B$. We study these mentioned notations which are generalization of the intuitionistic fuzzy essential (compliment) submodules, introduced by Basnet in [5]. Here we shall study some related results.
참고문헌 (15)
- E. A. Al-Dhaheri, "On Essential (Complement) Submodules with Respect to an Arbitrary Submodule", Iraqi Journal of Science, 59(2B), pp.904~908 (2018)
- F. W. Anderson, "Rings and Categories of Modules" (1992), Springer Verlag
- K. T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, pp.87~96 (1986)
- K. T. Atanassov, "Studies on Fuzziness and Soft Computing, 35" (1999), Physica-Verlag
- D. K. Basnet, "Topics in intuitionistic fuzzy algebra", Lambert Academis Publishing
- R. Biswas, "Intuitionistic fuzzy subgroup", Mathematical Forum X, pp.37~46 (1989)
- B. Davvaz, "Intuitionistic fuzzy Hv-submodules", Information Sciences, 176, pp.285~300 (2006)
- Kaur Gagandeep, "Intuitionistic fuzzy small submodule with respect to an arbitrary intuitionistic fuzzy submodule", CiiT International Journal of Fuzzy Systems, 10(10), pp.225~229 (2018)
- K. Hur, "Intuitionistic Fuzzy Subgroups and Subrings", Honam Math J, 25(1), pp.19~41 (2003)
- 허걸, "Intuitionistic Fuzzy Ideals of a Ring", 순수 및 응용수학, 12(3), pp.193~209 (2005), 한국수학교육학회
- Paul Isaac, "On Intuitionistic Fuzzy Submodules of a Module", Int. J. of Mathematical Sciences and Applications, 1(3), pp.1447~1454 (2011)
- S. Safaeeyan, "Essential submodules with respect to an arbitrary submodule", J. Mathematics Extension, 7(3), pp.15~27 (2013)
- P. K. Sharma, "(α,β)-Cut of intuitionistic fuzzy modules", Int. J. of Mathematical Sciences and Applications, 3(1), pp.1489~1492 (2011)
- P. K. Sharma, "Intuitionistic fuzzy superfluous modules", Notes on Intuitionistic Fuzzy Sets, 22(3), pp.34~46 (2016)
- P. K. Sharma, "Intuitionistic Fuzzy Prime Spectrum of a Ring", CiiT International Journal of Fuzzy Systems, 9(8), pp.167~175 (2017)