Ebook: Algebras, Rings and Modules: Volume 1

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." (José Gómez Torrecillas, Zentralblatt MATH, Vol. 1086 (12), 2006)

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Content:
Front Matter....Pages i-xii
Preliminaries....Pages 1-29
Decompositions of rings....Pages 30-58
Artinian and Noetherian rings....Pages 59-81
Categories and functors....Pages 82-110
Projectives, injectives and flats....Pages 111-142
Homological dimensions....Pages 143-160
Integral domains....Pages 161-188
Dedekind domains....Pages 189-209
Goldie rings....Pages 210-225
Semiperfect rings....Pages 226-261
Quivers of rings....Pages 262-299
Serial rings and modules....Pages 300-318
Serial rings and their properties....Pages 319-340
Semiperfect semidistributive rings....Pages 341-364
Back Matter....Pages 365-380

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Content:
Front Matter....Pages i-xii
Preliminaries....Pages 1-29
Decompositions of rings....Pages 30-58
Artinian and Noetherian rings....Pages 59-81
Categories and functors....Pages 82-110
Projectives, injectives and flats....Pages 111-142
Homological dimensions....Pages 143-160
Integral domains....Pages 161-188
Dedekind domains....Pages 189-209
Goldie rings....Pages 210-225
Semiperfect rings....Pages 226-261
Quivers of rings....Pages 262-299
Serial rings and modules....Pages 300-318
Serial rings and their properties....Pages 319-340
Semiperfect semidistributive rings....Pages 341-364
Back Matter....Pages 365-380
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