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Semigroup varieties closed for the Bruck extension

Published online by Cambridge University Press:  18 May 2009

Francis Pastijn  and
Xiaoying Yan
Francis Pastijn
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53233, USA
Xiaoying Yan
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53233, USA
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We shall show that there exists a chain, order isomorphic to the chain of real numbers, of semigroup varieties closed for the Bruck extension. The least semigroup variety closed for the Bruck extension will be obtained as the union of varieties in an infinite chain of semigroup varieties.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 371 - 380
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

1.Adjan, S. I., Identities in special semigroups, Dokl. Akad. Nauk SSSR 43 (1962), 499–502 (in Russian).Google Scholar
2.Blyth, T. S. and Janowitz, M. F., Residuation theory, (Pergamon Press, 1972).Google Scholar
3.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys 7, (Amer. Math. Soc, Providence, Vol. I, 1961; Vol. II, 1967).Google Scholar
4.Pastijn, F. and Yan, X., Completely regular semigroups in the variety generated by the bicyclic semigroup, Algebra Universalis, 30 (1993), 234–240.CrossRefGoogle Scholar
5.Pastijn, F. and Yan, X., Varieties of semigroups and varieties of completely regular semigroups closed for certain extensions, J. Algebra, 163 (1994), 777–794.CrossRefGoogle Scholar
6.Petrich, M., Inverse semigroups, (Wiley, 1984).Google Scholar
7.Rosenstein, J. G., Linear orderings, (Academic Press, 1982).Google Scholar