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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.
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Abstract

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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

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