Hostname: page-component-669899f699-cf6xr Total loading time: 0 Render date: 2025-04-26T21:24:29.703Z Has data issue: false hasContentIssue false
  • English
  • Français

Some saturated varieties of semigroups

Published online by Cambridge University Press:  17 April 2009

N.M. Khan
N.M. Khan
Affiliation:
Department of Mathematics, 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 show that a semigroup satisfying a heterotypical identity of which at least one side has no repeated variable is saturated and find sufficient conditions on a homotypical identity which is not a permutation identity and of which at least one side has no repeated variable, to ensure that any semigroup satisfying the identity is saturated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 3 , June 1983 , pp. 419 - 425
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]Higgins, P.M., “Saturated and epimorphically closed varieties of semigroups”, J. Austral. Math. Soc. Ser. A (to appear).Google Scholar
[4]Higgins, P.M., “The varieties of commutative semigroups for which epis are onto”, Proc. Edinburgh Math. Soc. (to appear).Google Scholar
[5]Higgins, Peter M., “A semigroup with an epimorphically embedded subband”, Bull. Austral. Math. Soc. 27 (1983), 231–242.CrossRefGoogle Scholar
[6]Howie, J.M., An introduction to semigroup theory (London Mathematical Society Monographs, 7. Academic Press, London, New York, San Francisco, 1976).Google Scholar
[7]Howie, J.M. and Isbell, J.R., “Epimorphisms and dominions. II”, J. Algebra 6 (1967), 7–21.CrossRefGoogle Scholar
[8]Isbell, John R., “Epimorphisms and dominions”, Proceedings of the conference on categorical algebra, La Jolla, 1965, 232–246 (Springer-Verlag, Berlin, Heidelberg, New York, 1966).CrossRefGoogle Scholar
[9]Khan, N.M., “Epimorphisms, dominions and varieties of semigroups”, Semigroup Forum 25 (1982), 331–337.CrossRefGoogle Scholar
[10]Khan, N.M., “On saturated permutative varieties and consequences of permutation identities”, J. Austral. Math. Soc. Ser. A (to appear).Google Scholar