On rings over which every flat module is finitely projective
Abdelhaq El Khalfi \,^1, Oussama Aymane Es-Safi\,^2 and Moutu Abdou Salam Moutui\,^3
\,^{1} Fundamental and Applied Mathematics Laboratory, Faculty of Sciences Ain Chock,
Hassan II University of Casablanca, Morocco.
\,^{2} Faculty of Science and Technology, Sidi Mohamed ben Abdellah University of Fez, Morocco.
\,^{3} Department of Mathematics and Statistics St. Francis Xavier University
Antigonish, Nova Scotia, Canada B2G 2W5.
.
Pages 239-247 | Received 14 August 2024, Accepted 28 March 2025, Published 26 January 2026
Abstract
The main goal of this paper is to investigate the class of rings for which every flat module is finitely projective (called FMF-ring, for short). We examine the stability of this property in several distinguished contexts of commutative ring extensions such as direct product, polynomial ring, power series ring, localization, homomorphic image, trivial ring extensions and amalgamation rings. Our results enrich the current literature with various new and original families of non-coherent, non-perfect, non-arithmetical and non-Noetherian rings that satisfying this property.
Keywords: FMF-ring, direct product, localization, homomorphic image, amalgamation of rings, trivial ring extension.
MSC numbers: Primary 13D05, 13D02.
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