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Congruences on Completely Regular Semigroups

Published online by Cambridge University Press:  20 November 2018

Mario Petrich
Mario Petrich*
Affiliation:
The University of Western Ontario, London, Ontario
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There are two subjects in the literature on semigroups which have recently attracted great attention: the class of completely regular semigroups (that is semigroups which are unions of their subgroups) and congruences on regular semigroups. In completely regular semigroups, the most popular subject is that of varieties, even though other aspects of them, such as structure, congruences, amalgamation, received their due attention. On the other hand, the treatment of congruences on regular semigroups became especially interesting with the emergence of the kernel-trace approach. This method proved quite successful in the case of inverse semigroups, see [6], whereas the analysis for the general regular semigroups encounters considerable difficulties, see [4].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 3 , 01 June 1989 , pp. 439 - 461
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Howie, J.M., An introduction to semigroup theory (Academic Press, London, 1976).Google Scholar
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3. Jones, P.R., Semilattice decompositions and the congruence lattice of semigroups (preprint).Google Scholar
4. Pastijn, F. and Petrich, M., Congruences on a regular semigroup, Trans. Amer. Math. Soc. 295 (1986), 607–633.Google Scholar
5. Petrich, M., Introduction to semigroups (Merrill, Columbus, 1973).Google Scholar
6. Petrich, M., Inverse semigroups (Wiley-Interscience, New York, 1984).Google Scholar
7. Petrich, M., A structure theorem for completely regular semigroups, Proc. Amer. Math. Soc. 99 (1987), 617–622.Google Scholar
8. Petrich, M., Congruences on strong semilattices of regular simple semigroups, Semigroup Forum 37 (1988), 167–199.Google Scholar