This paper deals with well-known notion of P F -rings, that is, rings in which principal ideals are flat. We give a new characterization of P F -rings. Also, we provide a necessary and sufficient condition for R ⊲⊳ I (resp., R/I when R is a Dedekind domain or I is a primary ideal) to be P F -ring. The article includes a brief discussion of the scope and precision of our results.2000 Mathematics Subject Classification. 13D05, 13D02.
In this paper, we study the class of rings in which every flat ideal is finitely projective. We investigate the stability of this property under localizations and homomorphic images, and its transfer to various contexts of constructions such as direct products, amalgamation of rings A f J , and trivial ring extensions. Our results generate examples which enrich the current literature with new and original families of non-coherent rings that satisfy this property.
We study the class of rings in which every P-flat module is flat. In domains this property characterizes Prüfer domains. We investigate the preservation of this property under localization, homomorphic image, direct product, amalgamation, and trivial ring extension. Our results yield examples which enrich the current literature with new and original families of rings that satisfy this property.
In this paper, we introduce the notion of "P-semihereditary rings" which is a generalization of the notion of semihereditary rings. We establish the transfer of this notion to trivial ring extensions and provide a class of P-semihereditary rings which are not a semihereditary rings.
Abstract. In this paper, we study the class of rings in which every P -flat ideal is singly projective. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as direct products, amalgamation of rings A f J, and trivial ring extensions. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.Mathematics Subject Classification (2010): 13D05, 13D02
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