Characterization of various (♭, ℓ) neutrosophic ideals of an ordered Γ-semigroups

A. Rajalakshmi, Nasreen Kausar, Brikena Vrioni*, K. Lenin Muthu Kumaran, Nezir Aydin, Murugan Palanikumar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce the notion of ♭, ℓ-neutrosophic subsemigroup (NSS), neutrosophic left ideal(NLI), neutrosophic right ideal(NRI), neutrosophic ideal (NI), neutrosophic bi-ideal(NBI), (ϵ, ϵ ∨ q)-neutrosophic ideal, neutrosophic bi-ideal of an ordered Γ-semigroups and discuss some of their properties. The concept of ♭, ℓ-neutrosophic ideal is a new extension of neutrosophic ideal over ordered Γ-semigroups Z. A non-empty subset ξ is a (♭, ℓ)-NSS (NLI, NRI, NBI, (1,2)-ideal) of Z. Then the lower level set ∆ is an subsemi-group (LI, RI, BI, (1, 2) − ideal) of Z, where ∆ = {ϱ ∈ Z|∆(ϱ) > ♭}, Ψ = {ϱ ∈ Z|∆(ϱ) > ♭} and ℧ = {ϱ ∈ Z|∆(ϱ) < ♭}. A subset ξ = [∆, Ψ, ℧] is a (♭, ℓ) − NSS[NLI, NRI, NBI, (1, 2) − ideal] of Z if and only if each non-empty level subset ξt is a subsemigroup [LI, RI, BI, (1, 2) − ideal] of Z for all t ∈ (♭, ℓ]. Every (ϵ, ϵ ∨ q)NBI of Z is a (♭, ℓ)NBI of Z, but converse need not be true and examples are provided to illustrate our results.

Original languageEnglish
Pages (from-to)325-337
Number of pages13
JournalInternational Journal of Neutrosophic Science
Volume25
Issue number2
DOIs
Publication statusPublished - 27 Jul 2024

Keywords

  • (ϵ, ϵ ∨ q) bi-ideals
  • (♭, ℓ) bi-ideals
  • Ordered Γ-semigroups
  • bi-ideals
  • neutrosophic ideals

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