## 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.## References

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## Additional Information

- © Copyright 1982 American Mathematical Society
- 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