A Course in Ring Theory
By addebook • Oct 3rd, 2008 • Category: Mathematics
A Course in Ring Theory (AMS Chelsea Publishing)
A Course in Ring Theory (AMS Chelsea Publishing)
By Donald S. Passman
Publisher: American Mathematical Society
Number Of Pages: 306
Publication Date: 2004-01
ISBN-10 / ASIN: 0821836803
ISBN-13 / EAN: 9780821836804
Binding: Hardcover
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.
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