Algebras, Rings and Modules Volume 1 [Hardcover]

Preliminaries.- Decompositions of rings.- Artinian and Noetherian rings.- Categories and functors.- Projectives, injectives and flats.- Homological dimensions.- Integral domains.- Dedekind domains.- Goldie rings.- Semiperfect rings.- Quivers of rings.- Serial rings and modules.- Serial rings and their properties.- Semiperfect semidistributive rings.

From the reviews of the first edition:

This is the first of two volumes which aim to take the theory of associative rings and their modules from fundamental definitions to the research frontier. The book is written at a level intended to be accessible to students who have taken standard basic undergraduate courses in linear algebra and abstract algebra. & has been written with considerable attention to accuracy, and has been proofread with care. & A very welcome feature is the substantial set of bibliographic and historical notes at the end of each chapter. (Kenneth A. Brown, Mathematical Reviews, 2006a)

This book follows in the footsteps of the valuable work done during the seventies of systematizing the investigation of properties and structure of rings by using their categories of modules. & A remarkable novelty in the present monograph is the study of semiperfect rings by means of quivers. & Another good idea is the inclusion of the study of commutative as well as non-commutative discrete valuation rings. Each chapter ends with some illustrative historical notes. (Jos? G?mez Torrecillas, Zentralblatt MATH, Vol. 1086 (12), 2006)

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