  In this paper, we define weakly coherent rings, and examine the transfer of
these rings to homomorphic image, trivial ring extension, localization, and
direct product. 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 by localization. Also, we show that the class of weakly coherent rings
and the class of strongly 2-coherent rings are not comparable.
