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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Coextensions of regular semigroups by rectangular bands. I

Authors: John Meakin and K. S. S. Nambooripad
Journal: Trans. Amer. Math. Soc. 269 (1982), 197-224
MSC: Primary 20M10
MathSciNet review: 637035
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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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Keywords: Regular semigroup, biordered set, regular partial band, idempotent-generated semigroup, coextension, recangular band
Article copyright: © Copyright 1982 American Mathematical Society