Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-04-30T18:37:25.433Z Has data issue: false hasContentIssue false
  • English
  • Français

On the lattice of congruences on a regular semigroup

Published online by Cambridge University Press:  17 April 2009

T. E. Hall
T. E. Hall
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria.
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.

A result of Reilly and Scheiblich for inverse semigroups is proved true also for regular semigroups. For any regular semigroup S the relation θ is defined on the lattice, Λ(S), of congruences on S by: (ρ, τ) ∈ θ if ρ and τ induce the same partition of the idempotents of S. Then θ is a congruence on Λ(S), Λ(S)/θ is complete and the natural homomorphism of Λ(S) onto Λ(S)/θ is a complete lattice homomorphism.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 2 , August 1969 , pp. 231 - 235
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, vols. 1 and 2, (Amer. Math. Soc. Mathematical Surveys 7, Providence, 1961 and 1967).Google Scholar
[2]Lallement, G., “Congruences et équivalences de Green sur un demi-groupe régulier”, C.R. Acad. Sc. Paris, Série A, 262 (1966), 613–616.Google Scholar
[3]Lallement, Gérard, “Demi-groupes réguliers” (Doctoral dissertation), Ann. Mat. Pura Appl. (IV), Vol. 77, (1967), 47–130.CrossRefGoogle Scholar
[4]Munn, W.D., “A certain sublattice of the lattice of congruences on a regular semigroup”, Proc. Cambridge Philos. Soc. 60 (1964), 385–391.CrossRefGoogle Scholar
[5]Reilly, N.R. and Scheiblich, H.E., “Congruences on regular semigroups”, Pacific J. Math. 23 (1967), 349–360.CrossRefGoogle Scholar