2013/06/12 by Engi̇n Büyükaşık, Engin Büyükaşık, Büyükaşık, Engin +2 · 1 citation
Mathematics · #16D10 #16D40 #16D70 #16E30 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AC #math.RA #msc:16D10 #msc:16D40 #msc:16D70 #msc:16E30
paper · pdf · doi:10.48550/arxiv.1306.2860
arxiv created 2013/06/12 · openalex publication_date 2013/06/12 · arxiv updated 2013/06/13 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let R be a ring and M be a right R-module. M is called neat-flat if any short exact sequence of the form 0→ K→ N→ M→ 0 is neat-exact i.e. any homomorphism from a simple right R-module S to M can be lifted to N. We prove that, a module is neat-flat if and only if it is simple-projective. Neat-flat right R-modules are projective if and only if R is a right ∑-CS ring. Every finitely generated neat-flat right R-module is projective if and only if R is a right C-ring and every finitely generated free right R-module is extending. Every cyclic neat-flat right R-module is projective if and only if R is right CS and right C-ring. Some characterizations of neat-flat modules are obtained over the rings whose simple right R-modules are finitely presented.