A Course in Ring Theory by Donald S. Passman (PDF)

Description

First published in 1991, this book contains the core material for an undergraduate first course in ring theory. Using the underlying theme of projective and injective modules, the author touches upon various aspects of commutative and noncommutative ring theory. In particular, a number of major results are highlighted and proved. The first part of the book, called “Projective Modules”, begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderburn, Artinian and Noetherian rings, hereditary rings, Dedekind domains, etc.). This part concludes with an introduction and discussion of the concepts of the projective dimension. Part II, “Polynomial Rings”, studies these rings in a mildly noncommutative setting. Some of the results proved include the Hilbert Syzygy Theorem (in the commutative case) and the Hilbert Nullstellensatz (for almost commutative rings). Part III, “Injective Modules”, includes, in particular, various notions of the ring of quotients, the Goldie Theorems, and the characterization of the injective modules over Noetherian rings. The book contains numerous exercises and a list of suggested additional reading. It is suitable for graduate students and researchers interested in ring theory.

User’s Reviews

Editorial Reviews: Review “…presentation is clear, the proofs are often quite ingenious and the exercises are well chosen … ” — MathSciNet

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is very nice one.It is “not too elementary”, and “not too advanced”.But, looking at its content, I think, it is better to consider this book for teaching to “undergraduates”. The topics are very specially selected and are very useful in advanced subjects such as “Algebraic Number Theory, Commutative Algebra, Algebraic Geometry, Modular Representation Theory, Local Fields, Homological Algebra” at least. I mean, this book contains those basic topics, which are “preliminary chapters” of each of the subject mentioned above.So highly recommended for M.Sc. completed Indian students.

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