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Certain characterizations of varieties of bands

Published online by Cambridge University Press:  20 January 2009

J. A. Gerhard  and
Mario Petrich
J. A. Gerhard
Affiliation:
Department of Mathematics, University of Manitoba, Manitoba, Canada
Mario Petrich
Affiliation:
Department of Mathematics, University of Manitoba, Manitoba, Canada
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The lattice of varieties of bands was constructed in [1] by providing a simple system of invariants yielding a solution of the world problem for varieties of bands including a new system of inequivalent identities for these varieties. References [3] and [5] contain characterizations of varieties of bands determined by identities with up to three variables in terms of Green's relations and the functions figuring in a construction of a general band. In this construction, the band is expressed as a semilattice of rectangular bands and the multiplication is written in terms of functions among these rectangular band components and transformation semigroups on the corresponding left zero and right zero direct factors.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 301 - 319
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Gerhard, J. A. and Petrich, M., Varieties of bands revisited, submitted.Google Scholar
2.Pastijn, F. and Petrich, M., Congruences on regular semigroups, Trans. Amer. Math. Soc. 295 (1986), 607–633.CrossRefGoogle Scholar
3.Petrich, M., A construction and a classification of bands, Math. Nachr. 48 (1971), 263–274.CrossRefGoogle Scholar
4.Petrich, M., Structure of completely regular semigroups, Trans. Amer. Math. Soc. 189 (1974), 211–236.CrossRefGoogle Scholar
5.Petrich, M., Lectures in Semigroups (Akademie-Verlag, Berlin, 1977).CrossRefGoogle Scholar
6.Petrich, M., A structure theorem for completely regular semigroups, Proc. Amer. Math. Soc. 99, (1987), 617–622.CrossRefGoogle Scholar