ADMISSIBLE (REES) EXACT SEQUENCES AND FLAT ACTS | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 2، فروردین 2025، صفحه 327-346 اصل مقاله (182.02 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12249.1648 | ||
| نویسندگان | ||
| Elahe Nafarieh Talkhooncheh1؛ Maryam Salimi* 2؛ Hamid Rasouli1؛ Elham Tavasoli2؛ Abolfazl Tehranian1 | ||
| 1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. | ||
| 2Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran. | ||
| 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 | ||
| مراجع | ||
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