Publication

Abstract : . A unit regular monoid S is said to be R− strongly unit regular if for any x, y ∈ S, xRy (where R is the Green’s relation) implies that there exists an element u in the group of units of S such that x = yu. The full transformation semigroup T (X) on a finite set X is seen to be R-strongly unit regular [4]. Hence the unit regular orthodox monoid ML exist for T (X) [10]. Let G(X) denote the group of units of T (X). For a L− class L of T (X), TL is defined to be TL = ∪e∈E(L)He which is the union of the group H− classes (where E(L) denote the set of idempotents of the L− class L). Also GL is a maximal subgroup of G(X) making TL ∪ GL an unit regular orthodox monoid and ML is defined to be TL ∪ GL [10]. Here we characterize the unit regular orthodox monoid ML of T (X). In the case of T (X) we also identify the minimal subgroup G1L of G(X) which makes TL ∪ G1L an unit regular orthodox monoid.