Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-15T11:24:47.354Z Has data issue: false hasContentIssue false

Semigroup varieties closed for the Bruck extension

Published online by Cambridge University Press:  18 May 2009

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

1.Adjan, S. I., Identities in special semigroups, Dokl. Akad. Nauk SSSR 43 (1962), 499502 (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), 234240.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), 777794.CrossRefGoogle Scholar
6.Petrich, M., Inverse semigroups, (Wiley, 1984).Google Scholar
7.Rosenstein, J. G., Linear orderings, (Academic Press, 1982).Google Scholar