ADMISSIBLE (REES) EXACT SEQUENCES AND FLAT ACTS

نویسندگان
Nafarieh Talkhooncheh, Elahe ID 1
Salimi, Maryam ID 2
Rasouli, Hamid ID 3
Tavasoli, Elham ID 4
Tehranian, Abolfazl ID 5

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran.

3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

4 Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran.

5 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

doi
10.22044/jas.2023.12249.1648
چکیده

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.

کلیدواژه‌ها
$S$-act, Rees exact sequence, admissible exact sequence, admissibly projective acts