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A Novel Method for Generating the M -Tri-Basis of an Ordered Γ -Semigroup

Author

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  • M. Palanikumar

    (Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India)

  • Chiranjibe Jana

    (Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India)

  • Omaima Al-Shanqiti

    (Department of Applied Science, Umm Al-Qura University, Mecca P.O. Box 24341, Saudi Arabia)

  • Madhumangal Pal

    (Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India)

Abstract

In this paper, we discuss the hypothesis that an ordered Γ -semigroup can be constructed on the M -left(right)-tri-basis. In order to generalize the left(right)-tri-basis using Γ -semigroups and ordered semigroups, we examined M -tri-ideals from a purely algebraic standpoint. We also present the form of the M -tri-ideal generator. We investigated the M -left(right)-tri-ideal using the ordered Γ -semigroup. In order to obtain their properties, we used M -left(right)-tri-basis. It was possible to generate a M -left(right)-tri-basis from elements and their subsets. Throughout this paper, we will present an interesting example of order ⪯ m l t ( ⪯ m r t ) , which is not a partial order of S . Additionally, we introduce the notion of quasi-order. As an example, we demonstrate the relationship between M -left(right)-tri-basis and partial order.

Suggested Citation

  • M. Palanikumar & Chiranjibe Jana & Omaima Al-Shanqiti & Madhumangal Pal, 2023. "A Novel Method for Generating the M -Tri-Basis of an Ordered Γ -Semigroup," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:893-:d:1063743
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