On weakly coherent rings

Abstract

In this paper, we define weakly coherent rings and examine the transfer of this property to homomorphic images, trivial ring extensions, localizations and finite direct products. These results provide examples of weakly coherent rings that are not coherent rings. We show that the class of weakly coherent rings is not stable under localization. Also, we show that the class of weakly coherent rings and the class of strongly $2$-coherent rings are not comparable.