Coextensions of regular semigroups by rectangular bands. I
John C. Meakin, K. S. S. Nambooripad · Transactions of the American Mathematical Society · 1982
This paper initiates a general study of the structure of a regular semigroup $S$ via the maximum congruence $\rho$ on $S$ with the property that each $\rho$-class $e\rho$, for $e = {e^2} \in S$, is a rectangular subband of $S$. Congruences of this type are studied and the maximum such congruence is characterized. A construction of all biordered sets which are coextensions of an arbitrary biordered set by rectangular biordered sets is provided and this is specialized to provide a construction of all solid biordered sets. These results are used to construct all regular idempotent-generated semigroups which are coextensions of a regular idempotent-generated semigroup by rectangular bands: a construction of normal coextensions of biordered sets is also provided.