admissible (rees) exact sequences and flat acts

Let $s$ be a commutative pointed monoid. in this paper, some properties of admissible (rees) short exact sequences of $s$-acts are investigated. in particular, it is shown that every admissible short exact sequence of $s$-acts is rees short exact. in addition, a characterization of flat acts via preserving admissible short exact sequences is established. as a consequence, we show that for a flat $s$-act $f$, the functor $f otimes_{s} -$ preserves admissible morphisms. finally, it is proved that the class of flat $s$-acts is a subclass of admissibly projective ones.