On regularities of ordered semigroups

Tiprachot, Nuchanat; Lekkoksung, Nareupanat; Pibaljommee, Bundit

doi:10.1142/s1793557122502072

Cited by 3 publications

(1 citation statement)

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“…In 2022, Chinram and Nakkhasen [2] studied properties of almost bi-quasi-interior ideals and their fuzzy bi-interior ideals in semigroups. In the same year, Gaketem [7] defined and gave properties of almost bi-interior ideals and fuzzy almost bi-interior ideals in semigroups, and, Tiprachot and Lekkoksung [12] studied almost α-ideals in semigroups. Moreover, the concepts of almost ideals be extended to study in another algebraic structure, for example, in ternary semigroups [11], in LA-semihypergroups [8], in Γ-semigroups [9], in Γ-semihypergroups [13].…”

Section: Introductionmentioning

confidence: 99%

Almost bi-quasi-ideals and their fuzzifications in semigroups

Thiti,

Ronnason

2023

AUCMCS

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The notion of bi-quasi-ideals of semigroups was introduced by Krishna Rao in 2017, which is a generalization of left ideals, right ideals, bi-ideals, and quasi-ideals of semigroups. In this paper, we introduce the concept of almost bi-quasi ideals as a generalization of bi-quasi ideals of semigroups. We investigate the properties of almost bi-quasi-ideals and fuzzy almost bi-quasi-ideals in semigroups. Moreover, we show some relationships between almost bi-quasi-ideals and fuzzy almost bi-quasi-ideals.

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Section: Introductionmentioning

confidence: 99%

Almost bi-quasi-ideals and their fuzzifications in semigroups

Thiti,

Ronnason

2023

AUCMCS

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Characterizations of ordered semigroups in terms of fuzzy (m, n)-substructures

Mahboob,

Al-Tahan,

Muhiuddin

2024

Soft Comput

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Characterizations of generalized fuzzy ideals in ordered semigroups

Davvaz

Chinram

Lekkoksung

et al. 2023

IFS

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Ideals play an essential part in studying ordered semigroups. There are several generalizations of ideals that are used to investigate ordered semigroups. It was known that (m, n)-ideals and n-interior ideals are an abstraction of bi-ideals and interior ideals, respectively. This paper introduces a generality of (m, n)-ideals and n-interior ideals, so-called (α, β)-fuzzy (m, n)-ideals and (α, β)-fuzzy n-interior ideals. Furthermore, we discuss our current notions with those that already exist. We examine connections between (m, n)- (resp., n-interior) ideals and (α, β)-fuzzy (m, n)- (resp., n-interior) ideals. A characterization of (α, β)-fuzzy (m, n)- (resp., n-interior) ideals, by a particular product, in ordered semigroups is provided. We demonstrate that our results generalize the known results through specific settings.

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On regularities of ordered semigroups

Abstract: In ordered semigroups, the notion of [Formula: see text]-ideals is a generalized concept of [Formula: see text]-ideals, where [Formula: see text]. We apply the notion of [Formula: see text]-ideals to characterize all regularities in ordered semigroups.

Cited by 3 publications

References 10 publications

Almost bi-quasi-ideals and their fuzzifications in semigroups

Almost bi-quasi-ideals and their fuzzifications in semigroups

Characterizations of ordered semigroups in terms of fuzzy (m, n)-substructures

Characterizations of generalized fuzzy ideals in ordered semigroups

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