Coextensions of regular semigroups by rectangular bands. I

Meakin, John; Nambooripad, K. S. S.

doi:10.1090/S0002-9947-1982-0637035-3

Coextensions of regular semigroups by rectangular bands. I
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by John Meakin and K. S. S. Nambooripad PDF

Trans. Amer. Math. Soc. 269 (1982), 197-224 Request permission

Abstract:

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.

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