Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-27T17:09:04.261Z Has data issue: false hasContentIssue false
  • English
  • Français

The varieties of commutative semigroups for which epis are onto

Published online by Cambridge University Press:  14 November 2011

P. M. Higgins
P. M. Higgins
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria, Australia 3168
Get access Rights & Permissions [Opens in a new window]

Synopsis

In a forthcoming paper, N. M. Khan gives a condition for a variety of commutative semigroups V to be saturated in the sense of Howie and Isbell (1967) (i.e. epis are onto for each S ∈ V). We show the necessity of the condition by constructing a non-saturated semigroup which is a member of every commutative variety not satisfying Khan's condition. This determination of the saturated varieties of commutative semigroups enables us then to prove that these varieties form a sublattice of the lattice of varieties of all commutative semigroups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 1 - 7
Copyright
Copyright © Royal Society of Edinburgh 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Clifford, A. H. and Preston, G. B.. The Algebraic Theory of Semigroups. Math. Surveys No. 7, Vol. I, 1961; Vol. II,1967. Providence, R. I.: Amer. Math. Soc.Google Scholar
2Hall, T. E. and Jones, P. R.. Epis are onto for finite regular semigroups. Proc. Edinburgh Math. Soc. to appear.Google Scholar
3Howie, J. M.. An introduction to semigroup theory. London Math. Soc. Monographs 7 (London: Academic Press, 1976).Google Scholar
4Howie, J. M. and Isbell, J. R.. Epimorphisms and dominions II. J. Algebra 6 (1967), 7–21.CrossRefGoogle Scholar
5Isbell, J. R.. Epimorphisms and dominions. Proceedings of the Conference on Categorical Algebra, La Jolla, 1965, 232–246. Berlin: Lange & Springer, 1966.Google Scholar
6Khan, N. M.. Epimorphisms, dominions and varieties of semigroups. Semigroup Forum to appear.Google Scholar
7Mitchell, B.. Theory of Categories (London: Academic Press, 1965).Google Scholar