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XII.—The Lattice of Congruences on a Bisimple ω-Semigroup*

Published online by Cambridge University Press:  14 February 2012

W. D. Munn
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow.
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Synopsis

A necessary and sufficient condition is determined for the modularity of the lattice of congruences on a bisimple inverse semigroup whose semilattice of idempotents is order-anti-isomorphic to the set of natural numbers.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 67 , Issue 3 , 1967 , pp. 175 - 184
Copyright
Copyright © Royal Society of Edinburgh 1967

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References

References to Literature

Clifford, A. H., and Preston, G. B., 1961. “The algebraic theory of semigroups, Vol. 1”. Math. Surv., 7.Google Scholar
Howie, J. M., 1964. “The maximum idempotent-separating congruence on an inverse semigroup,” Proc. Edin. Math. Soc., 14, 71–79.Google Scholar
Kurosh, A. G., 1963. Lectures on general algebra. (English translation, New York.)Google Scholar
Munn, W. D., and Reilly, N. R., 1966. “Congruences on a bisimple ω-semi-group”, Proc. Glasg. Math. Ass., 7, 184–192.CrossRefGoogle Scholar
Reilly, N. R., 1966. “Bisimple ω-semigroups”, Proc. Glasg. Math. Ass., 7, 160–167.Google Scholar