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.
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