Publication Type:

Journal Article

Source:

Southeast Asian Bulletin of Mathematics, Volume 40, Issue 1, p.125-129 (2016)

Keywords:

Maximal subgroup, Minimal subgroup, Orthodox monoid., Transformation semigroup, Unit regular semigroup

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.

Cite this Research Publication

Dr. Sreeja V. K., “Characterization of Some Unit Regular Orthodox Submonoids of the Full Transformation Semigroup T(X)”, Southeast Asian Bulletin of Mathematics, vol. 40, no. 1, pp. 125-129, 2016.