The provided text is the preface and table of contents of the book "Lectures on Modules and Rings" by T. Y. Lam, published by Springer-Verlag in 1999. The book is part of the Graduate Texts in Mathematics series and covers advanced topics in ring theory, with a focus on modules. The preface begins with a reflection on the challenges of writing a textbook and the author's motivation for completing this work. It also acknowledges the contributions of various individuals who helped with the book's development.
The table of contents outlines the structure of the book, which is divided into 19 sections across 7 chapters. The sections cover topics such as free modules, projective and injective modules, flat modules, homological dimensions, uniform dimensions, singular submodules, dense submodules, rational hulls, rings of quotients, classical rings of quotients, right Goldie rings, Artinian rings of quotients, maximal rings of quotients, Martindale rings of quotients, Frobenius and quasi-Frobenius rings, matrix rings, Morita theory, and Morita duality theory.
The book assumes a basic understanding of elementary ring theory and references the author's previous work, "A First Course in Noncommutative Rings," for foundational concepts. It includes extensive exercises and a comprehensive list of notations and abbreviations to aid readers in their study.The provided text is the preface and table of contents of the book "Lectures on Modules and Rings" by T. Y. Lam, published by Springer-Verlag in 1999. The book is part of the Graduate Texts in Mathematics series and covers advanced topics in ring theory, with a focus on modules. The preface begins with a reflection on the challenges of writing a textbook and the author's motivation for completing this work. It also acknowledges the contributions of various individuals who helped with the book's development.
The table of contents outlines the structure of the book, which is divided into 19 sections across 7 chapters. The sections cover topics such as free modules, projective and injective modules, flat modules, homological dimensions, uniform dimensions, singular submodules, dense submodules, rational hulls, rings of quotients, classical rings of quotients, right Goldie rings, Artinian rings of quotients, maximal rings of quotients, Martindale rings of quotients, Frobenius and quasi-Frobenius rings, matrix rings, Morita theory, and Morita duality theory.
The book assumes a basic understanding of elementary ring theory and references the author's previous work, "A First Course in Noncommutative Rings," for foundational concepts. It includes extensive exercises and a comprehensive list of notations and abbreviations to aid readers in their study.