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The Least Commutative Congruence on a simple regular ω-semigroup†

Published online by Cambridge University Press:  18 May 2009

C. Bonzini ,
A. Cherubini  and
B. Piochi
C. Bonzini
Affiliation:
Dipartimento di Matematica, Universitá, Via Saldini, 50 20133 Milano.
A. Cherubini
Affiliation:
Dipartimento di Matematica, Universitá, Via del Capitano, 15 53100 Siena.
B. Piochi
Affiliation:
Dipartimento di Matematica, Politecnico, Piazza L. da Vinci, 32 20133 Milano.
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Piochi in [10] gives a description of the least commutative congruence γ of an inverse semigroup in terms of congruence pairs and generalizes to inverse semigroups the notion of solvability. The object of this paper is to give an explicit construction of λ for simple regular ω-semigroups exploiting the work of Baird on congruences on such semigroups. Moreover the connection between the solvability classes of simple regular ω-semigroups and those of their subgroups is studied.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 1 , January 1990 , pp. 13 - 23
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Ault, J. E., Group congruences on a bisimple ω-semigroup, Semigroup Forum 10 (1975), 351–366.Google Scholar
2.Baird, G. R., On a sublattice of the lattice of congruences on a simple regular ω-semigroup, J. Austral. Math. Soc. 13 (1972), 461–471.Google Scholar
3.Baird, G. R., Congruences on simple regular ω-semigroups, J. Austral. Math. Soc. 14 (1972), 155–167.CrossRefGoogle Scholar
4.Bonzini, C. and Cherubini, A., The least commutative congruence on a regular ω-semigroup, Quaderno n. 21/1987, Dipartimento di Matematica dell' Universita' di Milano.Google Scholar
5.Kocin, B. P., The structure of inverse ideally simple ω-semigroups, Vestnik Leningrad Univ. 237 (1968), 41–50.Google Scholar
6.Munn, W. D., Regular ω-semigroups, Glasgow Math. J. 9 (1968), 46–66.Google Scholar
7.Munn, W. D. and Reilly, N. R., Congruences on a bisimple ω-semigroup, Proc. Glasgow Math. Ass., 7 (1966), 184–192.Google Scholar
8.Petrich, M., Congruences on simple ω-semigroups, Glasgow Math. J. 20 (1979), 87–101.Google Scholar
9.Petrich, M., Inverse semigroups (Wiley & Sons, 1984).Google Scholar
10.Piochi, B., Solvability in inverse semigroups, Semigroup Forum 34 (1987), 287–303.Google Scholar
11.Piochi, B., The least commutative congruence on bisimple ω-semigroup, Rapp. Dip. Mat. Univ. Siena, 158 (1987), 1–14.Google Scholar