A regular semigroup S is said to bo orthodox if for any e, f ∈ E(S), ef ∈ E(S) where E(S) denotes the set of idempotents of S. A regular monoid S is said to be unit regular if for any x ∈ S, there exists an element u in the group of units of S such that x = xux. Here we characterize some orthodox unit regular submonoids associated with the L−class and R− class of a R−strongly (L−strongly) unit regular monoid.
Dr. Sreeja V. K. and Rajan, A. R., “Construction of Certain Unit Regular Orthodox Submonoids”, Southeast Asian Bulletin of Mathematics, vol. 38, no. 6, pp. 907–916, 2014.