Examines properties of admissible Rees exact sequences in S-acts, highlighting implications for 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 ⊗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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Talkhooncheh et al. (2023) studied this question.
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