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.
Highlights
All rings considered in this paper are assumed to be commutative with identity elements and all modules are unitary
We start by recalling a few definitions
P -flatness coincides with torsion-freeness in the sense of [12]
Summary
All rings considered in this paper are assumed to be commutative with identity elements and all modules are unitary. As in [3], an R-module M is called singly projective if, for any cyclic submodule N of M , the inclusion map N → M factors through a free module F. We are interested in rings over which every P -flat ideal is singly projective. We investigate the stability of the F SP -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 original examples which enrich the current literature with new families of rings satisfying the F SP -property
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