CONSTRUCTION OF A R -STRONGLY UNIT REGULAR MONOID FROM A REGULAR BIORDERED SET AND A GROUP
Akhila Rajan, V K Sreeja · Asian-European Journal of Mathematics · 2011
In this paper we give a detailed study of R-strongly unit regular monoids. The relations between the biordered set of idempotents and the group of units in unit regular semigroups are better identified here. Conversely, starting from a regular biordered set E and a group G we construct a R-strongly unit regular semigroup S for which the set of idempotents E(S) is isomorphic to E as a biordered set and the group of units G(S) is isomorphic to G. The conditions to be satisfied by G and E are also listed.