Vol. 107, No. 2, 1983

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Absolutely flat semigroups

Sydney Dennis Bulman-Fleming and K. McDowell

Vol. 107 (1983), No. 2, 319–333
Abstract

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.

Mathematical Subject Classification 2000
Primary: 20M20
Milestones
Received: 6 October 1981
Revised: 11 June 1982
Published: 1 August 1983
Authors
Sydney Dennis Bulman-Fleming
K. McDowell