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 G 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 . Hence the unit regular orthodox monoid QR exists for T (X) . Let G(X) denote the group of units of T (X). For an R-class R of a R-strongly unit regular monoid S, ZR is defined to be ∪e∊E(R)(HG)e, where E(R) denote the set of idempotents in the R-class R and (HG)e denote the HG class containing e. (Here the equivalence HG is defined on the monoid S as xHGy if and only if x = yu and x = u'y for some unit u, u' in G.) Then QR = ZR ∪G'R (See the Remark after Theorem 1.2) is an unit regular orthodox submonoid of S. Here we characterize the unit regular orthodox monoid QR of T (X). [ABSTRACT FROM AUTHOR]
Dr. Sreeja V. K., “Orthodox Unit Regular Submonoids of the Full Transformation Semigroup T(X)”, Southeast Asian Bulletin of Mathematics, vol. 39, pp. 711 - 715, 2015.