These types of rings can be viewed as descendants of algebras examined by Georg Frobenius.
A partial list of pioneers in quasi-Frobenius rings includes R. Brauer, K. Morita, T. Nakayama, C. J. Nesbitt, and R. M. Thrall.
With additional assumptions, these definitions can also be used to generalize QF rings.
A few other mathematicians pioneering these generalizations included K. Morita and H. Tachikawa.
Following (Anderson & Fuller 1992), let R be a left or right Artinian ring: The numbering scheme does not necessarily outline a hierarchy.