A monoid S with group of units G is said to be regular if for each x ∈ S, there is an element a ∈ S such that x = xax. We consider arbitrary monoids and describe various properties depending on the group of units. Properties of regular monoids and description of some special classes of regular monoids are also given. [ABSTRACT FROM AUTHOR]
Dr. Sreeja V. K. and Rajan, A. R., “Some Properties of Regular Monoids”, Southeast Asian Bulletin of Mathematics, vol. 39, pp. 891 - 902, 2015.