Abstract
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].
Publisher
Sociedade Paranaense de Matematica
Reference22 articles.
1. Abbasi, M. Y. and Basar Abul, On Ordered Quasi-Gamma-Ideals of Regular Ordered Gamma-Semigroups, Algebra, 2013, Article ID 565848,(2013). doi:10.1155/2013/565848
2. Abbasi, M. Y. and Basar Abul, Some properties of ordered 0-minimal (0; 2)-bi--ideals in po--semigroups, Hacettepe Journal of Mathematics and Statistics, 44(2) (2015),247 -254.
3. Abbasi, M. Y. and Basar Abul, A note on ordered quasi--ideals in intra-regular po-- semigroups, International Journal of Pure and Applied Mathematics, 2(98) (2015),221-230.
4. Akram, M. , N. Yaqoob, N. and Khan, M., On (m,n)-ideals in LA-semigroups, Applied Mathematical Sciences, 7(44) (2013) 2187-2191.
5. Amjad, V., Hila, K. and Yousafzai, F., Generalized hyperideals in locally associative left almost semihypergroups, New York Journal of Mathematics, 20 (2014) 1063–1076.