On (m, n, Γ)-REGULAR,(m, 0, Γ)-SIMPLE, (0,n, Γ)-SIMPLE AND (m, n, Γ)-SIMPLE le-Γ-SEMIGROUPS

摘要

In this paper, we first show that, in le-Γ-semigroups, γB+m~n? Bγ,γ Q_m~n? Qγ and γH_m~n? H_γ. We, then, show that, in (m,n,γ)-regular le-Γ-semigroups, B_γ = Q_γ = H_γ = γB_m~n = γQ_m~n = γH_m~n and characterize (m,n,γ)-regular le-Γ-semigroups in terms of (m, n, γ)-ideal elements. Finally, we introduce and characterize (m, 0, Γ)- simple, (0,n, Γ)-simple and (m, n, Γ)-simple poe-Γ-semigroups and also show that, in (m, n, Γ)-simple le-Γ-semigroups, L_γ = R_γ = B_γ = Q_γ = H_γ = mI_γ = γI_n = γB_m~n = yQ_m~n =γH_m~n= S × S.