Quasi-interior ideals and fuzzy quasi-interior ideals of $\Gamma$-semigroups
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, as a further generalization of ideals, we introduce the notion of a quasi interior ideal as a generalization of ideals, quasi ideals, bi-ideals and interior ideals of $\Gamma$-semigroups and study their properties. We characterize the quasi-interior simple $\Gamma$-semigroup and regular $\Gamma$-semigroup using quasi-interior ideals of $\Gamma$-semigroups. We introduce the notion of fuzzy quasi-interior ideals of a $\Gamma$-semigroup and study fuzzy quasi-interior ideals properties of a $\Gamma$-semigroup.
Abstract
In this paper, as a further generalization of ideals, we introduce the notion of a quasi interior ideal as a generalization of ideals, quasi ideals, bi-ideals and interior ideals of $\Gamma$-semigroups and study their properties. We characterize the quasi-interior simple $\Gamma$-semigroup and regular $\Gamma$-semigroup using quasi-interior ideals of $\Gamma$-semigroups. We introduce the notion of fuzzy quasi-interior ideals of a $\Gamma$-semigroup and study fuzzy quasi-interior ideals properties of a $\Gamma$-semigroup.
참고문헌 (15)
- N. Nobusawa, "On a generalization of the ring theory", Osaka. J. Math, 1, pp.81~89 (1964)
- M. Murali Krishna Rao, "Γ-semirings-I", Southeast Asian Bull. Math, 19(1), pp.49~54 (1995)
- M. K. Sen, "On Γ−semigroup", Proc. of International Conference of algebra and its application, pp.301~308 (1981), Decker Publicaiton
- R. A. Good, "Associated groups for a semigroup", Bull. Amer. Math. Soc, 58, pp.624~625 (1952)
- S. Lajos, "On the bi-ideals in associative ring", Proc. Japan Acad, 46, pp.505~507 (1970)
- O. Steinfeld, "Uher die quasi ideals", Von halbgruppend Publ. Math. Debrecen, 4, pp.262~275 (1956)
- K. Is´eki, "Ideal theory of semigroup", Proc. Japan Acad, 32, pp.554~559 (1956)
- L. A. Zadeh, "Fuzzy sets", Information and control, 8, pp.338~353 (1965)
- A. Rosenfeld, "Fuzzy groups", J. Math. Anal. Appl, 35, pp.512~517 (1971)
- U. M. Swamy, "Fuzzy prime ideals of rings", Jour. Math. Anal. Appl, 134, pp.94~103 (1988)
- W. J. Liu, "Fuzzy invariant subgroups and fuzzy ideals", Fuzzy sets and Systems, 8(2), pp.133~139 (1982)
- M. Murali Krishna Rao, "bi-interior Ideals in semirings", Discussiones Mathematicae General Algebra and Applications, 38, pp.69~78 (2018)
- M. Murali Krishna Rao, "Bi-quasi-ideals and fuzzy bi-quasi ideals of Γ-semigroups", Bull. Int. Math. Virtual Inst, 7(2), pp.231~242 (2017)
- M. Murali Krishna Rao, "Quasi-interior ideals and weak interior ideals", Asia Pacific Journal of Math, pp.7~21 (2020)
- M. Murali Krishna Rao, "Bi-interior ideals and Fuzzy bi-interior ideals of Γ-semigroups", Ann. Fuzzy Math. Inform, 24(1), pp.85~100 (2022)