A Course in Ring Theory
Donald S. Passman
Genre
Science & Nature
Format
Hardcover
Dimensions
7.20 (w) x 10.20 (h) x 0.90 (d)
Pages
306
Publisher
American Mathematical Society
Publication Date
September 2004
ISBN
9780821836804
Book ISBN 10
0821836803
About Book
Reviews
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. Part I, 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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