Title of article :
ADMISSIBLE (REES) EXACT SEQUENCES AND FLAT ACTS
Author/Authors :
Nafarieh Talkhooncheh ، Elahe Department of Mathematics - Islamic Azad University, Science and Research Branch , Salimi ، Maryam Department of Mathematics - Islamic Azad University, East Tehran Branch , Rasouli ، Hamid Department of Mathematics - Islamic Azad University, Science and Research Branch , Tavasoli ، Elham Department of Mathematics - Islamic Azad University, East Tehran Branch , Tehranian ، Abolfazl Department of Mathematics - Islamic Azad University, Science and Research Branch
Abstract :
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.
Keywords :
Rees exact sequence , admissible exact sequence , admissibly projective acts , $S$ , act
Journal title :
Journal of Algebraic Systems
Journal title :
Journal of Algebraic Systems
