## A network of congruences on an inverse semigroup

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- by Mario Petrich and Norman R. Reilly PDF
- Trans. Amer. Math. Soc.
**270**(1982), 309-325 Request permission

## Abstract:

A congruence $\rho$ on an inverse semigroup $S$ is determined uniquely by its kernel and its trace. Denoting by ${\rho ^{\min }}$ and ${\rho _{\min }}$ the least congruence on $S$ having the same kernel and the same trace as $\rho$, respectively, and denoting by $\omega$ the universal congruence on $S$, we consider the sequence $\omega$, ${\omega ^{\min }}$, ${\omega _{\min }}$, ${({\omega ^{\min }})_{\min }}$, ${({\omega _{\min }})^{\min }} \ldots$. These congruences, together with the intersections of corresponding pairs, form a sublattice of the lattice of all congruences on $S$. We study the properties of these congruences and establish several properties of the quasivarieties of inverse semigroups induced by them.## References

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## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**270**(1982), 309-325 - MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9947-1982-0642343-6
- MathSciNet review: 642343