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The kernel and trace operators for ideal extensions of regular semigroups

Published online by Cambridge University Press:  18 May 2009

Mario Petrich
Mario Petrich
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, CanadaN6A 5B7
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Abstract

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Let V be a regular semigroup and an ideal extension of a semigroup S by a semigroup Q Congruences on V can be represented by triples of the form (σ, P, τ), here called admissible, where a is a congruence on S, P is an ideal of Q and τ is a O-restricted congruence on Q/P satisfying certain conditions. We characterize the trace relation T on V in terms of admissible triples. When the extension V of S is strict, for a congruence v on V given in terms of an admissible triple, we characterize vK, vK, vT and vT again in terms of admissible triples.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 2 , May 1994 , pp. 219 - 231
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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