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The congruence lattice of an ideal extension of semigroups

Published online by Cambridge University Press:  18 May 2009

Mario Petrich
Mario Petrich
Affiliation:
Dipartimento di MatematiceUniversitá di Lecce73160 LecceItaly
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Let S be an ideal of a semigroup V. In such a case, V is an (ideal) extension of S by T = V/S. The problem considered in [2] is the construction of all congruences on V in terms of congruences on S and T. This did not succeed for all congruences but it did for those congruences whose restriction to S is weakly reductive. If the extension is strict, more precise constructions are also given there. With some relatively weak restrictions on S, we are able to obtain in this way all congruences on V in the form indicated above.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 1 , January 1993 , pp. 39 - 50
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

1.Clifford, A. H., Extensions of semigroups, Trans. Amer. Math. Soc. 68 (1950), 165–173.CrossRefGoogle Scholar
2.Petrich, M., Congruences on extensions of semigroups, Duke Math. J. 34 (1967), 215–224.CrossRefGoogle Scholar
3.Petrich, M., Inverse semigroups (Wiley-Interscience, New York, 1984).Google Scholar
4.Petrich, M., The congruence lattice of an extension of completely 0-simple semigroups (preprint).Google Scholar