Absolutely flat semigroups

Sydney Dennis Bulman-Fleming and K. McDowell

Vol. 107 (1983), No. 2, 319–333

DOI: 10.2140/pjm.1983.107.319

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