Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T07:44:21.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Homomorphisms and congruences on ωα-bisimple semigroups

Published online by Cambridge University Press:  09 April 2009

J. W. Hogan
J. W. Hogan
Affiliation:
Marshall UniversityHuntington, West Virginia, U. S. A.
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.

Let S be a bisimple semigroup, let Es denote the set of idempotents of S, and let ≦ denote the natural partial order relation on Es. Let ≤ * denote the inverse of ≦. The idempotents of S are said to be well-ordered if (Es, ≦ *) is a well-ordered set.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 4 , June 1973 , pp. 441 - 460
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, Vol. I (Math. Surveys No. 7, Amer. Math. Soc., Providence, 1961).Google Scholar
[2]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, Vol. II. (Math. Surveys No. 7, Amer. Math. Soc., Providence, 1967).Google Scholar
[3]Clifford, A. H., ‘A Class of d-Simple Semigroups’, Amer. J. Math. 75 (1953), 547–556.CrossRefGoogle Scholar
[4]Hogan, J. W., ‘Bisimple Semigroups with Idempotents Well-ordered’, (To appear).Google Scholar
[5]Sierpinski, Waclaw, Cardinal and Ordinal Numbers (Second Ed. Revised, Panstwowe Wydawnictwo Naukowe (PWN — Polish Scientific Publishers), Warszawa (Poland), 1965).Google Scholar
[6]Warne, R. J., ‘Matrix Representation of d-Simple Semigroups’, Trans. Amer. Math. Soc. 106 (1963), 427–435.Google Scholar
[7]Warne, R. J., ‘Homomorphisms of d-Simple Semigroups with Identity,’ Pacific J. Math. 14 (1964), 1111–1122.CrossRefGoogle Scholar
[8]Warne, R. J., ‘A Class of Bisimple Inverse Semigroups,’ Pacific J. Math. 18 (1966), 563–577.CrossRefGoogle Scholar
[9]Warne, R. J., ‘The Idempotent Separating Congruences of a Bisimple Inverse Semigroup’, Publicationes Mathematicae, 13 (1966), 203–206.Google Scholar
[10]Warne, R. J., ‘Bisimple Inverse Semigroups Mod Groups,’ Duke Math. J. 34 (1967), 787–811.CrossRefGoogle Scholar
[11]Warne, R. J., ‘Congruences on ωn -Bisimple Semigroups,’ J. Australian Math. Soc. 9 (1969), 257–274.Google Scholar