S-almost semisimple rings

The aim of this paper is to characterize multiplicative subsets S and commutative rings R for which every R-module is strongly flat with respect to S. Commutative rings R for which all R-modules are strongly flat with respect to S are characterized by the following two conditions: the ring \(R_S\) $R_S$ is semisimple, and, for every element \(s \in S\) $s\in S$ , the ring R/sR is semisimple as well. Rings satisfying these conditions are called S-almost semisimple. The paper provides new characterizations of semisimple rings in terms of strongly flat R-modules. Moreover, we give some examples to distinguish von Neumann regular rings, semisimple rings, and S-almost semisimple rings.