Absolutely flat semigroups
Sydney Bulman‐Fleming, Kenneth McDowell · Pacific Journal of Mathematics · 1983
All left modules over a ring are flat if and only if the ring is von Neumann regular.In [7], M. Kilp showed that for a monoid S to be left absolutely flat (i.e., for all left S-sets to be flat) regularity is necessary but not sufficient.Kilp also proved [8] that every inverse union of groups is absolutely flat.In the present paper we show that in fact every inverse semigroup is absolutely flat and that the converse is not true.PROPOSITION 2.7.Homomorphic images of (left, right) absolutely flat monoids are {left, right) absolutely flat.