Pullbacks and flatness properties of acts. II

In two papers by Laan (Acta Comment. Univ. Tartu. Math. 2 (1998) 55-60; Com m. Algebra 29 (2000) 00-00) studies were initiated of flatness properties o f right acts As over a monoid S that can be described in terms of when the functor As circle times - preserves pullbacks. In those articles, familiar flatness properties emerged in a new light, and new properties were discove red. The present paper continues this investigation. Three additional flatn ess properties are obtained, and the "homological classification" problem-F or which monoids S do all right S-acts have a certain flatness property? - is discussed for all of the new properties under consideration.