On a generalization of strong flatness

Strong flatness or flatness of right acts over a monoid S has been the topic of many papers on homological classification of monoids during the last decades. It has turned out to be useful to consider a property called condition (P), which lies strictly between these two properties. In this paper we define a new condition (O) and show that the class of S-acts satisfying this condition lies strictly between the classes of strongly flat S-acts and S-acts satisfying condition (P).