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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0637035-3
PII: S 0002-9947(1982)0637035-3
Keywords: Regular semigroup, biordered set, regular partial band, idempotent-generated semigroup, coextension, recangular band
Article copyright: © Copyright 1982 American Mathematical Society