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Abstract
The operators hn and i n and their duals hmacr;n and imacr;n defined on the free semigroup X + for a nonempty set X by Gerhard and Petrich are proved here to be homomorphisms of onto certain subsets of X + with a suitable multiplication. From the work of the authors mentioned, these operators induce fully invariant congruences on X + corresponding to join irreducible varieties of bands if X is countably infinite. New operators on X + are defined by means of these operators which give homomorphisms in an analogous way and induce fully invariant congruences on X +corresponding to all varieties of bands except for the variety of all bands, and some varieties of normal bands. The former of these was investigated by the mentioned authors and the latter must be treated differently. By means of the above operators we are able to characterize all cases of relatively free bands.
∗Supported by F.C.T. and PRAXIS XXI/BCC/4358/94
†Supported by F.C.T. and Project AGC/PRAXIS XXI/2/2.1/MAT/63/94
∗Supported by F.C.T. and PRAXIS XXI/BCC/4358/94
†Supported by F.C.T. and Project AGC/PRAXIS XXI/2/2.1/MAT/63/94
Notes
∗Supported by F.C.T. and PRAXIS XXI/BCC/4358/94
†Supported by F.C.T. and Project AGC/PRAXIS XXI/2/2.1/MAT/63/94