Quasi-Frobenius rings and Nakayama rings were introduced by T
Nakayama in 1939. Since then, these classical artinian rings have
continued to fascinate ring theorists with their abundance of
properties and structural depth. In 1978, M Harada introduced a new
class of artinian rings which were later called Harada rings in his
honour. Quasi-Frobenius rings, Nakayama rings and Harada rings are
very closely interrelated. As a result, from a new perspective, we
may study the classical artinian rings through their interaction
and overlap with Harada rings. The objective of this seminal work
is to present the structure of Harada rings and provide important
applications of this structure to the classical artinian rings. In
the process, we cover many topics on artinian rings, using a wide
variety of concepts from the theory of rings and modules. In
particular, we consider the following topics, all of which are
currently of much interest and ongoing research: Nakayama
permutations, Nakayama automorphisms, Fuller's theorem on i-pairs,
artinian rings with self-duality, skew-matrix rings, the
classification of Nakayama rings, Nakayama group algebras, the
Faith conjecture, constructions of local quasi-Frobenius rings,
lifting modules, and extending modules. In our presentation of
these topics, the reader will be able to retrace the history of
artinian rings.
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