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ABSTRACT
Based on the operators and
and their duals
and
defined on the free semigroup
for a nonempty set
by Gerhard and Petrich, we introduce here the operators
which are proved to be homomorphisms of
onto certain subsets of
with suitable multiplication. These operators induce fully invariant congruences on
corresponding to most of the varieties of bands if X is countably infinite. Variants of operators
and
introduced by the cited authors are used here to elucidate the structure of relatively free bands for most band varieties in conjunction with the operators
. The few remaining varieties are treated separately.
ACKNOWLEDGMENTS
The first author was supported by F.C.T. and PRAXIS XXI/BCC/4358/94. The second author was supported by F.C.T. and Project AGC/PRAXIS XXI/2/2.1/MAT/63/94.