Characterization of weakly regular S-acts

We generalize the concept of weakly regularity in semigroups to S-acts,where S is a monoid. We prove among other results that if a monoidis von-Neumann regular then weakly regularity and von-Neumann regularity, in the context of S-acts, coincide. We also define locally projective S-acts, which is the generalization of projective S-acts. Weconsider many relationships between weakly regular S-acts and locallyprojective S-acts.