Rings in which every S-finitely presented ideal is finitely presented

In this paper, we introduce a new class of rings in which every S-finitely presented ideal is finitely presented called SWC-rings. Hence, a ring is coherent if and only if it is S-coherent and an SWC-ring. We study the transfer of this notion to various context of commutative ring extensions such as direct product, trivial ring extensions and pullbacks. Our results generate families of examples of non-S-coherent SWC-rings and non-SWC S-coherent rings.