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.

کلیدواژه ها:

S-act ، Rees exact sequence ، admissible exact sequence ، admissibly projective acts