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On left absolutely flat bands

1987
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Proceedings of the American Mathematical Society
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A semigroup S is called (left, right) absolutely flat if all of its (left, right) S-sets are flat. Let S = [_J{S~, : 7 6 T} be the least semilattice decomposition of a band S. It is known that if S is left absolutely flat then S is right regular (that is, each S7 is right zero). In this paper it is shown that, in addition, whenever a, ß 6 T, a < ß, and F is a finite subset of S3 x Sß, there exists w 6 Sa such that (wu,wv) € 6r{F) for all (u,v) € F (6r(F) denotes the smallest right congruence on

doi:10.1090/s0002-9939-1987-0911019-x
fatcat:cufm5eyfxrgr3gczkeknwsztmu