Mathematics and Statistics Vol. 9(3), pp. 302 - 308
DOI: 10.13189/ms.2021.090311
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Almost Interior Gamma-ideals and Fuzzy Almost Interior Gamma-ideals in Gamma-semigroups

Wichayaporn Jantanan ¹, Anusorn Simuen ², Winita Yonthanthum ², Ronnason Chinram ^2,*
1 Department of Mathematics, Faculty of Science, Buriram Rajabhat University, Buriram 31000, Thailand
² Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand

ABSTRACT

Ideal theory plays an important role in studying in many algebraic structures, for example, rings, semigroups, semirings, etc. The algebraic structure Г-semigroup is a generalization of the classical semigroup. Many results in semigroups were extended to results in Г-semigroups. Many results in ideal theory of Г-semigroups were widely investigated. In this paper, we first focus to study some novel ideals of Г-semigroups. In Section 2, we define almost interior Г-ideals and weakly almost interior Г-ideals of Г-semigroups by using the concept ideas of interior Г-ideals and almost Г-ideals of Г-semigroups. Every almost interior Г-ideal of a Г-semigroup S is clearly a weakly almost interior Г-ideal of S but the converse is not true in general. The notions of both almost interior Г-ideals and weakly almost interior Г-ideals of Г-semigroups are generalizations of the notion of interior Г-ideal of a Г-semigroup S. We investigate basic properties of both almost interior Г-ideals and weakly almost interior Г-ideals of Г-semigroups. The notion of fuzzy sets was introduced by Zadeh in 1965. Fuzzy set is an extension of the classical notion of sets. Fuzzy sets are somewhat like sets whose elements have degrees of membership. In the remainder of this paper, we focus on studying some novelties of fuzzy ideals in Г-semigroups. In Section 3, we introduce fuzzy almost interior Г-ideals and fuzzy weakly almost interior Г-ideals of Г-semigroups. We investigate their properties. Finally, we give some relationship between almost interior Г-ideals [weakly almost interior Г-ideals] and fuzzy almost interior Г-ideals [fuzzy weakly almost interior Г-ideals] of Г-semigroups.

KEYWORDS
Almost Interior Г-ideals, Weakly Almost Interior Г-ideals, Fuzzy Almost Г-interior Ideals, Fuzzy Weakly Almost Interior Г-ideals

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Wichayaporn Jantanan , Anusorn Simuen , Winita Yonthanthum , Ronnason Chinram , "Almost Interior Gamma-ideals and Fuzzy Almost Interior Gamma-ideals in Gamma-semigroups," Mathematics and Statistics, Vol. 9, No. 3, pp. 302 - 308, 2021. DOI: 10.13189/ms.2021.090311.

(b). APA Format:
Wichayaporn Jantanan , Anusorn Simuen , Winita Yonthanthum , Ronnason Chinram (2021). Almost Interior Gamma-ideals and Fuzzy Almost Interior Gamma-ideals in Gamma-semigroups. Mathematics and Statistics, 9(3), 302 - 308. DOI: 10.13189/ms.2021.090311.