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

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