On Relation Q_γ in le-Γ-Semigroups

Abstract

In this paper we introduce and study the relation Q_γ in le-Γ-
semigroups. This relation in general turns out to have better properties than
the relation H_γ studied in [2]. We give several properties that hold in every
Q_γ-class of an le-Γ-semigroup and especially in every Q_γ-class satisfying the
Green's condition. In particular, the γ-regularity and γ-intra-regularity of a
Q_γ-class is studied. We also consider a case a Q -class of an le-Γ-semigroup
M forms a subsemigroup of M_γ= (M;ο).