2021/03/26 by Wei Qi, Xiaolei Zhang, Qi, Wei +3 · 1 citation
Mathematics · #13B30 #13D05 #13E05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2103.14240
openalex publication_date 2021/03/26 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28
In this paper, we introduce and study the class S-F-ML of S-Mittag-Leffler modules with respect to all flat modules. We show that a ring R is S-coherent if and only if S-F-ML is closed under submodules. As an application, we obtain the S-version of Chase Theorem: a ring R is S-coherent if and only if any direct product of R is S-flat if and only if any direct product of flat R-modules is S-flat. Consequently, we provide an answer to the open question proposed by D. Bennis and M. El Hajoui [3].