In [2], Fuchs and Viljoen introduced and classified the $B^{*}$-modules for a valuation ring R: an R-module M is a $B^{*}$-module if $Ex{t}_R^1(M,X)=0$ for each divisible module X and each torsion module X with bounded order. The concept of a $B^{*}$-module was extended to the setting of a torsion theory over an associative ring in [14]. In the present paper, we use categorical methods to investigate the $B^{*}$-modules for a group graded ring. Our most complete result (Theorem 4.10) characterizes $B^{*}$-modules for a strongly graded ring R...

Let Fl(R) denote the category of flat right modules over an associative ring R. We find necessary and sufficient conditions for Fl(R) to be a Grothendieck category, in terms of properties of the ring R.