## Algebras, Rings and Modules, Volume 2As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined. The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provide the theory of semiprime Noetherian semiperfect and semidistributive rings. Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest. |

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### Contents

Quivers and their representations | 53 |

Appendix to section 2 5 More about Dynkin and extended | 105 |

Representations of posets and of finite dimensional | 113 |

Frobenius algebras and quasiFrobenius rings | 161 |

Right serial rings | 219 |

Tiled orders over discrete valuation rings | 255 |

Gorenstein matrices | 327 |

385 | |

397 | |

### Other editions - View all

Algebras, Rings and Modules, Volume 1 Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko Limited preview - 2004 |

Algebras, Rings and Modules, Volume 1 Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko Limited preview - 2006 |

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### References to this book

Groups, Rings and Group Rings Antonio Giambruno,Cesar Polcino Milies,Sudarshan K. Sehgal Limited preview - 2006 |