Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-27T11:03:39.607Z Has data issue: false hasContentIssue false

A semigroup with an epimorphically embedded subband

Published online by Cambridge University Press:  17 April 2009

Peter M. Higgins
Affiliation:
Monash University, Clayton, Victoria 3168, Australia.
Rights & Permissions [Opens in a new window]

Abstract

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 construct a semigroup S with an epimorphically embedded proper subband U. The band U furnishes an example of a regular semigroup which is not saturated, thus answering a question posed by Hall, Semigroup Forum (to appear).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Volume I (Mathematical Surveys, 7. American Mathematical Society, Providence, Rhode Island, 1961).Google Scholar
[2]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Volume II (Mathematical Surveys, 7. American Mathematical Society, Providence, Rhode Island, 1967).Google Scholar
[3]Gardner, B.J., “Epimorphisms of regular rings”, Comment Math. Univ. Carolin. 16 (1975), 151160.Google Scholar
[4]Hall, T.E., “Epimorphisms and dominions”, Semigroup Forum 24 (1982), 271283.CrossRefGoogle Scholar
[5]Hall, T.E. and Jones, P.R., “Epis are onto for finite regular semigroups”, Proc. Edinburgh Math. Soc. (to appear).Google Scholar
[6]Higgins, P.M., “Epis are onto for generalised inverse semigroups”, Semigroup Forum 23 (1981), 255259.CrossRefGoogle Scholar
[7]Higgins, Peter M., “The varieties of commutative semigroups for which epis are onto”, Proc. Edinburgh Math. Soc. (to appear).Google Scholar
[8]Higgins, P.M., “Saturated and epimorphically closed varieties of semigroups”, J. Austral. Math. Soc. Ser. A (to appear).Google Scholar
[9]Howie, J.M., An introduction to semigroup theory (London Mathematical Society Monographs, 7. Academic Press, London, New York, San Francisco, 1976).Google Scholar
[10]Howie, J.M. and Isbell, J.R., “Epimorphisms and dominions. II”, J. Algebra 6 (1967), 721.CrossRefGoogle Scholar
[11]Isbell, John R., “Epimorphisms and dominions”, Proceedings of the conference on categorical algebra, La Jolla, 1965, 232246 (Springer-Verlag, Berlin, Heidelberg, New York, 1966).CrossRefGoogle Scholar
[12]Khan, N.M., “Epimorphisms, dominions and varieties of semigroups”, Semigroup Forum (to appear).Google Scholar