A NOTE ON ORDERED QUASI-Gamma-IDEALS IN INTRA-REGULAR PO-Gamma-SEMIGROUPS

Abbasi, Mohammad Yahya; Basar, Abul

doi:10.12732/ijpam.v98i2.5

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“…for all a, b, x ∈ S and α, β ∈ Γ. For other basic definitions and properties, we refer [1], [8], [2], [3], [11], [13], [14], [16]. In what follows we denote the ordered Γ-semigroup (S, Γ, •, ≤) by S unless otherwise specified.…”

Section: Introductionmentioning

confidence: 99%

A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals

Abbasi

Basar

Ali

2021

bspm

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In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is shown that if (S,Γ,·,≤) is an ordered Γ-semigroup; m,n are non-negative integers and A(m,n) is the set of all ordered (m,n)-Γ-ideals of S. Then, S is (m,n)-regular⇐⇒ ∀A ∈ A(m,n), A = (AmΓSΓAn]. It is also proved that if (S,Γ,·,≤) is an ordered Γ-semigroup and m,n are nonnegative integers and R(m,0) and L(0,n) is the set of all (m,0)-Γideals and (0,n)-Γ-ideals of S, respectively. Then, S is (m,n)-regular ordered Γ semigroup ⇐⇒∀R ∈R(m,0)∀L ∈L(0,n),R∩L = (RmΓL∩RΓLn].

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