A note on regular semigroups with inverse transversals (Q1068207)

For a regular semigroup S with an inverse transversal \(S\circ\) the sets \(I=\{e\in S:\) \(e=ee^{\circ}\}\) and \(\Lambda =\{f\in S:\) \(f=f\circ f\}\) need not be subsemigroups of S. Assuming that they are, a theorem is proved describing the structure of S in terms of I, \(\Lambda\) and collections of mappings \(I\to I\), \(\Lambda\) \(\to \Lambda\).