Structure of coextensions of regular semigroups by rectangular bands. (Q1432823)

A coextension of a regular semigroup \(S\) is a pair \((T,\theta)\), where \(T\) is a regular semigroup and \(\theta\colon T \to S\) is a surjective homomorphism. Moreover, \((T,\theta)\) is a coextension of \(S\) by rectangular bands, if the inverse image \(e\theta^{-1}\) is a rectangular subband of \(T\) for each idempotent \(e\) of \(S\). The author gives a characterization of the structure of coextensions by regular bands.