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

Mohammad Yahya Abbasi | Zendy; Abul Basar | Zendy; Akbar Ali | Zendy

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

Author(s) -

Mohammad Yahya Abbasi,

Abul Basar,

Akbar Ali

Publication year - 2020

Publication title -

boletim da sociedade paranaense de matemática

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.347

H-Index - 15

eISSN - 2175-1188

pISSN - 0037-8712

DOI - 10.5269/bspm.41186

Subject(s) - mathematics , semigroup , combinatorics , characterization (materials science) , partially ordered set , discrete mathematics , physics , optics

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 = (A ΓSΓA]. It is also proved that if (S,Γ, ·,≤) is an ordered Γ-semigroup; m,n are nonnegative integers; R(m,0); L(0,n) is the set of all (m, 0)-Γ-ideals 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 = (RΓL ∩ RΓL].

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