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

DOI:
https://doi.org/10.1090/S0002-9947-1982-0637035-3

MathSciNet review:
637035

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Abstract: This paper initiates a general study of the structure of a regular semigroup via the maximum congruence on with the property that each -class , for , is a rectangular subband of . 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:
https://doi.org/10.1090/S0002-9947-1982-0637035-3

Keywords:
Regular semigroup,
biordered set,
regular partial band,
idempotent-generated semigroup,
coextension,
recangular band

Article copyright:
© Copyright 1982
American Mathematical Society