Subpullbacks and Po-flatness Properties of S-posets

In (Golchin A. and Rezaei P., Subpullbacks and flatness properties of S-posets. Comm. Algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. In this article first of all we describe po-flatness properties of -posets over pomonoids by po-surjectivity of  corresponding to certain subpullback diagrams. Then we introduce three new Conditions ,  and  and investigate the relation between them and Conditions , , , ,  and . Also we describe these properties by po-surjectivity of  corresponding to certain subpullback diag
In (Golchin A. and Rezaei P., Subpullbacks and flatness properties of S-posets. Comm. Algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. In this article first of all we describe po-flatness properties of -posets over pomonoids by po-surjectivity of  corresponding to certain subpullback diagrams. Then we introduce three new Conditions ,  and  and investigate the relation between them and Conditions , , , ,  and . Also we describe these properties by po-surjectivity of  corresponding to certain subpullback diagrams and describe Conditions ,  and  by weak po-surjectivity of  corresponding to certain subpullback diagrams.
rams and describe Conditions ,  and  by weak po-surjectivity of  corresponding to certain subpullback diagrams.