WATTS THEOREMS FOR ASSOCIATIVE RINGS

Let R be an associative ring. In this paper we consider the category CMod-R of right R-modules M such that M ? Hom _R (R, M) and the category DMod-R of right R-modules M such that M ? _R R ? M. Given two associative rings R and R′, we study the functors F : CMod-R → CMod-R′ that can be written as Hom _R (P, ?) and the functors G : DMod-R → DMod-R′ that can be written as – ? _R Q and we give some results that extend the known Watts theorems for rings with identity to associative rings that need not be unital.