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

M. Palanikumar, Chiranjibe Jana (), Omaima Al-Shanqiti and Madhumangal Pal
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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

Mathematics, 2023, vol. 11, issue 4, 1-13

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.

Keywords: left tri-ideal; right tri-ideal; M-left-tri-basis; M-right-tri-basis; quasi-order; partial order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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