On regular semigroups and their multiplication
Pierre Antoine Grillet · Transactions of the American Mathematical Society · 1978
A method is given for the construction of regular semigroups in terms of groups and partially ordered sets. This describes any regular semigroup S and its multiplication by means of triples ( i , g , λ ) \left ( {i,\,g,\,\lambda } \right ) with i ∈ S / R i\, \in \,S/{\mathcal {R}} , λ ∈ S / L \lambda \, \in \,S/{\mathcal {L}} and g in the Schützenberger group of the corresponding D {\mathcal {D}} -class. It is shown that the multiplication on S is determined by certain simple products. Furthermore the associativity of these simple products implies associativity of the entire multiplication.