Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T13:48:03.992Z Has data issue: false hasContentIssue false

On saturated permutative varieties and consequences of permutation identities

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

N. M. Khan
Affiliation:
Department of Mathematics Monash UniversityClayton, Victoria, Australia3168
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 determine which permutative varieties are saturated and classify all nontrivial permutation identities for the class of all globally idempotent semigroups.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys 7, Amer. Math. Soc., Providence, R.I., vol. I; 1961, vol. II, 1967.Google Scholar
[2]Higgins, P. M., ‘The commutative varieties of semigroups for which epis are onto’, Proc. Edinburgh Math. Soc., to appear.Google Scholar
[3]Higgins, P. M., ‘Saturated and epimorphically closed varieties of semigroups’, J. Austral. Math. Soc., to appear.Google Scholar
[4]Howie, J. M., An introduction to semigroup theory (London Math. Soc. Monographs 7, Academic Press, 1976).Google Scholar
[5]Howie, J. M. and Isbell, J. R., ‘Epimorphisms and dominions II’, J. Algebra 6 (1967), 721.CrossRefGoogle Scholar
[6]Isbell, J. R., ‘Epimorphisms and dominions’, Proceedings of the Conference on Categorical Algebra, La Jolla, 1965, pp. 232246 (Lange and Springer, Berlin, 1966).Google Scholar
[7]Khan, N. M., ‘Epimorphisms, dominions and varities of semigroups’, Semigroup Forum 25 (1982), 331337.Google Scholar
[8]Khan, N. M., ‘Epimorphically closed permutative varities’, submitted.Google Scholar
[9]Perkins, P., ‘Bases for equation theories of semigroups’. J. Algebra 11 (1969), 298314.Google Scholar
[10]Putcha, M. S. and Yaqub, A., ‘Semigroups satisfying permutation identities’, Semigroup Forum 3 (1971), 6873.Google Scholar
[11]Yamada, M., ‘Regular semigroups whose idempotents satisfy permutation identities’, Pacific J. Math. 21 (1967), 371392.Google Scholar