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Multiplicative theory of ideals, Volume 43 (Pure and Applied Mathematics)
Multiplicative theory of ideals, Volume 43 (Pure and Applied Mathematics)
Date: 10 June 2011, 02:47

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The viability of the theory of commutative rings is evident from the many papers on the subject which are published each month. This is not surprising, considering the many problems in algebra and geometry, and indeed in almost every branch of mathematics, which lead naturally to the study of various aspects of commutative rings. In this book we have tried to provide the reader with an introduction to the basic ideas, results, and techniques of one part of the theory of commutative rings, namely, multiplicative ideal theory.
The text may be divided roughly into three parts. In the first part, the basic notions and technical tools are introduced and developed. In the second part, the two great classes of rings, the Prufer domains and the Krull rings, are studied in some detail. In the final part, a number of generalizations are considered. In the
appendix a brief introduction is given to the tertiary decomposition of ideals of noncommutative rings.
The lengthy bibliography begins with a list of books, some on commutative rings and others on related subjects. Then follows a list of papers, all more or less concerned with the subject matter of the text.
This book has been written for those who have completed a course in abstract algebra at the graduate level. Preceding the text there is a discussion of some of the prerequisites which we consider necessary.

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