The condition that weak injectivity is equivalent to injectivity is known as the Baer Criterion for injectivity. However, although this condition is true for injectivity of R-modules for every ring R with unit, it is not true for injectivity of S-acts, for an arbitrary monoid S. For example consider (N;max) (see Kilp et al., 2000). Seeking a characterization for the Baer Criterion to hold for acts over a monoid, Ebrahimi, Mahmoudi and Moghaddasi Angizan (2005, 2007) found some classes of monoids such that for acts over them the Baer Criterion holds. Also, it has been proved that in the category Pos-S of right S-posets, weak dc-injectivity does not imply dc-injectivity. Here we nd some classes of pomonoids satisfying this condition. First, we introduce the notion of S-completeness for S-posets which is weaker than weak dc-injectivity. This notion plays an important role to get through the Baer Criterion.
