Abstract
If AFB is an extension of semigroups, then the dominion of A in B, Dom(A,B), is the set of all bεB such that for each semigroup C and for each pair of homomorphisms f,g: B → C with f|A = g|A, then f(b) = g(b). It will be shown that epimorphisms are onto homomorphisms in the category of all bands with maximum conditions on D-classes. This contradicts an earlier report of a finite band B with a proper subband A such that Dom(A,B) = B. An example will be presented of a finite band B and a subband A such that Ac+Dom(A, B).
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Communicated by R. McFadden
TO ALFRED H. CLIFFORD
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Scheiblich, H.E. On epics and dominions of bands. Semigroup Forum 13, 103–114 (1976). https://doi.org/10.1007/BF02194926
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DOI: https://doi.org/10.1007/BF02194926