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Congruences on orthodox semigroups II

Published online by Cambridge University Press:  09 April 2009

John Meakin
John Meakin
Affiliation:
The University of Florida Gainesville, Florida and The University of NebraskaLincoln, Nebraska
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If ρ is a congruence on a regular semigroup S, then the kernel of ρ is defined to be the set of ρ-classes which contain idempotents of S. Preston [7] has proved that two congruences on a regular semigroup coincide if and only if they have the same kernel: this naturally poses the problem of characterizing the kernel of a congruence on a regular semigroup and reconstructing the congruence from its kernel. In some sense this problem has been resolved by the author in [5]. Using the well-known theorem of M. Teissier (see for example, A. H. Clifford and G. B. Preston [1], Vol. II, Theorem 10.6), it is possible to characterize the kernel of a congruence on a regular semigroup S as a set A = {Ai: i ∈ I} of subsets of S which satisfy the Teissier-Vagner-Preston conditions:

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 259 - 266
Copyright
Copyright © Australian Mathematical Society 1972

References

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