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Congruences on simple ω-semigroups

Published online by Cambridge University Press:  18 May 2009

Mario Petrich
Affiliation:
Université de Montpellier, France
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An inverse semigroup whose idempotents form an ω-chain e0 > e1 > e2 > … is called briefly an ω-semigroup. A structure theorem for simple ω-semigroups was established by Kočin [7]; a related structure theorem for simple, and also general, ω-semigroups was proved by Munn [10]. These results represent an extension of the structure theorem for bisimple a ω-semigroups due to Reilly [14].

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

1.Ault, J. E., Group congruences on a bisimple ωsemigroup, Semigroup Forum 10 (1975), 351366.CrossRefGoogle Scholar
2.Baird, G. R., On a sublattice of the lattice of congruences on a simple ω-semigroup, J. Austral. Math. Soc. 13 (1972), 461471.CrossRefGoogle Scholar
3.Baird, G. R., Congruences on simple ω-semigroups, J. Austral. Math. Soc. 14 (1972), 155167.CrossRefGoogle Scholar
4.Clifford, A. H., Semigroups admitting relative inverses, Ann. of Math. 42 (1941), 10371049.CrossRefGoogle Scholar
5.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 1, Math. Surveys No. 7, Amer. Math. Soc. (Providence, R. I., 1961).Google Scholar
6.Howie, J. M., An introduction to semigroup theory (Academic Press, 1976).Google Scholar
7.Kočin, B. P., Structure of inverse ideally-simple ω-semigroups, Vestnik Leningrad. Univ. Mat. Meh. Astronom. 23, No. 7 (1968), 4150 (Russian).Google Scholar
8.Kočin, B. P., On congruences on ideally simple inverse to ω-semigroups, The 21st Hercen Lectures, Leningrad. Gos. Ped. Inst. Učen. Zap. (1968), 1920 (Russian).Google Scholar
9.Munn, W. D., The lattice of congruences on a bisimple to ω-semigroup, Proc. Roy. Soc. Edinburgh 67 (1966), 175184.Google Scholar
10.Munn, W. D., Regular ω-semigroups, Glasgow Math. J. 9 (1968), 4666.CrossRefGoogle Scholar
11.Munn, W. D., On simple inverse semigroups, Semigroup Forum 1 (1970), 6374.CrossRefGoogle Scholar
12.Munn, W. D. and Reilly, N. R., Congruences on a bisimple ω-semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 184192.CrossRefGoogle Scholar
13.Petrich, Mario, Congruences on inverse semigroups, J. Algebra 55 (1978), 231256.CrossRefGoogle Scholar
14.Reilly, N. R., Bisimple ω-semigroups, Proc. Glasgow Math. Assoc. 7 (1966), 160167.CrossRefGoogle Scholar