Minimal Reversible Nonsymmetric Rings

Marks showed that F 2 Q 8 , the F 2 group algebra over the quaternion group, is a reversible nonsymmetric ring, then questioned whether or not this ring is minimal with respect to cardinality. In this work, it is shown that the cardinality of a minimal reversible nonsymmetric ring is indeed 256. Furthermore, it is shown that although F 2 Q 8 is a duo ring, there are also examples of minimal reversible nonsymmetric rings which are nonduo.