Monocyclic And Flatness Of Rees Factor Order S-systems

Let S be a pomonoid.In the first chapter,we mainly study the flatness prop-erties of a monocyclic S-posets.The emphasis is on the flatness of monocyclic left S-posets S/λ(1,x).The characterization of monocyclic left S-posets satisfying con-dition(P),strongly flat,free and projective are given.It is proved that the projec-tivity and strong flatness of monocyclic left S-posets are consistent.In the second part of this paper,we give some new generalizations on the flatness of Rees factor left S-posets,and give the equivalent characterization that the weakly torsion free Rees factor left S-posets satisfy the condition(PWP),condition(PWP)w,condition(WP),GP-flatness,GP-po-flatness,etc.This paper gives a comparatively complete answer to the problem of homological classification of weakly torsion S-posets.