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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 25 , Issue 2 , PP: 325-337, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups

A. Rajalakshmi 1 , Nasreen Kausar 2 , Brikena Vrioni 3 * , K. Lenin Muthu Kumaran 4 , Nezir Aydin 5 , Murugan Palanikumar 6

  • 1 Department of Mathematics, Shanmuga Industries Arts and Science College, Affiliated to Thiruvalluvar University, Tiruvannamalai, Tamil Nadu, 606603, India - (pearlakshmi03@gmail.com)
  • 2 Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler, 34220, Istanbul, Turkey - (kausar.nasreen57@gmail.com)
  • 3 School of Arts and Sciences, American International University, Kuwait - (Brikena.vrioni@yahoo.com)
  • 4 Department of Mathematics, Shanmuga Industries Arts and Science College, Affiliated to Thiruvalluvar University, Tiruvannamalai, Tamil Nadu, 606603, India - (leninmuthukumaran@gmail.com)
  • 5 College of Science and Engineering Hamad Bin Khalifa University, 34110 Doha, Qatar; Department of Industrial Engineering, Yildiz Technical University, Besiktas, 34349, Istanbul, Turkey - (naydin@hbku.edu.qa)
  • 6 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India - (palanimaths86@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.250228

    Received: January 10, 2024 Revised: March 16, 2024 Accepted: April 17, 2024
    Abstract

    In this paper, we introduce the notion of $\flat,\ell$-neutrosophic subsemigroup (NSS), neutrosophic left ideal(NLI), neutrosophic right ideal(NRI), neutrosophic ideal (NI), neutrosophic bi-ideal(NBI), $(\epsilon, \epsilon \vee q)$-neutrosophic ideal, neutrosophic bi-ideal of an ordered $\Gamma$-semigroups and discuss some of their properties. The concept of $\flat,\ell$-neutrosophic ideal is a new extension of neutrosophic ideal over ordered $\Gamma$-semigroups $\mathcal{Z}$. A non-empty subset $\xi_{\flat}$ is a $(\flat, \ell)$-NSS (NLI, NRI, NBI, (1,2)-ideal) of $\mathcal{Z}$. Then the lower level set $\Delta_{\flat}$ is an subsemigroup $(LI, RI, BI, (1,2)-ideal)$ of $\mathcal{Z}$, where $\Delta_{\flat}=\{\varrho\in \mathcal{Z}|\Delta(\varrho)> \flat\}$, $\Psi_{\flat}=\{\varrho\in \mathcal{Z} |\Delta(\varrho)> \flat\}$ and $\mho_{\flat}=\{\varrho\in \mathcal{Z}|\Delta(\varrho)< \flat\}$. A subset $\xi=[\Delta,\Psi,\mho]$ is a $(\flat, \ell)- NSS[NLI,NRI,NBI,(1, 2)-ideal]$ of $\mathcal{Z}$ if and only if each non-empty level subset $\xi_{t}$ is a subsemigroup $[LI,RI,BI,(1,2)-ideal]$ of $\mathcal{Z}$ for all $t\in(\flat, \ell]$. Every $(\epsilon, \epsilon \vee q)$NBI of $\mathcal{Z}$ is a $(\flat,\ell)$NBI of $\mathcal{Z}$, but converse need not be true and examples are provided to illustrate our results.

    Keywords :

    Ordered &Gamma , -semigroups , neutrosophic ideals , bi-ideals , (♭, ℓ) bi-ideals , (ϵ, ϵ &or , q) bi-ideals

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    Cite This Article As :
    Rajalakshmi, A.. , Kausar, Nasreen. , Vrioni, Brikena. , Lenin, K.. , Aydin, Nezir. , Palanikumar, Murugan. Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 325-337. DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi, A. Kausar, N. Vrioni, B. Lenin, K. Aydin, N. Palanikumar, M. (2025). Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science, (), 325-337. DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi, A.. Kausar, Nasreen. Vrioni, Brikena. Lenin, K.. Aydin, Nezir. Palanikumar, Murugan. Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science , no. (2025): 325-337. DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi, A. , Kausar, N. , Vrioni, B. , Lenin, K. , Aydin, N. , Palanikumar, M. (2025) . Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science , () , 325-337 . DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi A. , Kausar N. , Vrioni B. , Lenin K. , Aydin N. , Palanikumar M. [2025]. Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science. (): 325-337. DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi, A. Kausar, N. Vrioni, B. Lenin, K. Aydin, N. Palanikumar, M. "Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups," International Journal of Neutrosophic Science, vol. , no. , pp. 325-337, 2025. DOI: https://doi.org/10.54216/IJNS.250228

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