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# Algebras, Rings and Modules

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## Benefits

Contains almost all of the most important results in the theory of representations of posets, quivers and their applications to the representations of finite groups and finite dimensional algebras, most of them are given with full proof

Includes the most important results in the theory of quasi-Frobenius and right serial rings

In particular, gives the algorithm of the construction of a finite Frobenius ring by means of a finite partially ordered set and it is provides the proof of the Cartan Determinant Conjecture for right serial Artinian rings

Gives the full description of semiprime Noetherian semiperfect and semidistributive rings. In particular, with any finite poset it may be associated a prime Noetherian semiperfect and semidistributive ring with nonzero Jacobson radical and a finite ergodic Markov chain

Gives the description of semiprime Noetherian semiperfect and semidistributive rings of injective dimension at most one

Uses the technique of quivers to study of special classes of rings such as quasi-Frobenius rings and right serial rings

Discusses the properties of global dimension of different classes of rings

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Part of the Mathematics and Its Applications book series (MAIA, volume 586)