A MONOID OVER WHICH ALL CYCLIC FLAT RIGHT S-ACTS SATISFY CONDITION (E)

Although the properties of flatness and condition (E) for Sacts over a monoid S are incomparable, Liu([10]) showed that necessary and sufficient condition for a monoid S over which all left S-acts that satisfy condition (E) are flat is the regularity of S. But the problem of describing a monoid over which all cyclic flat left S-acts satisfy condition (E) is still open. Thus the purpose of this paper is to characterize monoids over which all cyclic flat right S-acts satisfy condition (E).