Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-09T01:40:28.498Z Has data issue: false hasContentIssue false
  • English
  • Français

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
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.

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.

Information

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

References

REFERENCES

1.Howie, J. M., An introduction to semigroup theory (Academic Press, 1976).Google Scholar
2.Pastijn, F. and Petrich, M., Congruences on regular semigroups, Trans. Amer. Math. Soc. 295 (1986), 607–633.Google Scholar
3.Petrich, M., Congruences on extensions of semigroups, Duke Math. J. 34 (1967), 215–224.Google Scholar
4.Petrich, M., The congruence lattice of an ideal extension of semigroups, Glasgow Math. J. 35 (1993), 39–50.CrossRefGoogle Scholar