“…It is well-known that a non-simple regular w-semigroup S is either an oj-chain of groups or the disjoint union of a finite chain of groups H = [n, Hj, </> ; ] and a simple regular ^-semigroup K = K(d, K t , ^,) which is an ideal of 5. In the latter case, as in [3,4], we will use the notation S = S([n, Hj, # y ]; K, 4>) where <f> is the homomorphism which induces the retract extension of K by H°, and which is actually a homomorphism of H into K o .…”