Abstract.  

Suppose R is a finite ring with an anti-isomorphism.  I will discuss how the anti-isomorphism allows one to view left R-modules as right R-modules, and vice versa.  Then I will discuss the problem of finding a left R-module with the property that its (right) character module, when viewed as a left module via the anti-isomorphism, is isomorphic to the original module.  In particular, the ring itself, viewed as a left module, has this property if and only if the ring is Frobenius.  Various examples will be given.