This volume is designed to serve as an introduction to the basic ideas and techniques of ring theory. It is intended to be an expository textbook, rather than a treatise on the subject. The mathematical background required for a proper understanding of the contents is not extensive. We assume that the average reader has had some prior contact with abstract algebra but is still relatively inexperienced in this respect. In consequence, nearly everything herein can be read by a person familiar with basic group-theoretic concepts and having a nodding acquaintance with linear algebra. The level of material should prove suitable for advanced undergraduates and beginning graduate students.
Author(s): David M. Burton
Edition: 0
Publisher: Addison-Wesley Educational Pub
Year: 1970
Language: English
Pages: 309
Ch 1 Introductory Concepts
Ch 2 Ideals and Their Operations
Ch 3 The Classical Isomorphism Theorems
Ch 4 Integral Domains and Fields
Ch 5 Maximal, Prime, and Primary Ideals
Ch 6 Divisibility Theory in Integral Domains
Ch 7 Polynomial Rings
Ch 8 Certain Radicals of a Ring
Ch 9 Two Classic Theorems
Ch 10 Direct Sums of Rings
Ch 11 Rings with Chain Conditions
Ch 12 Further Results on Noetherian Rings
Ch 13 Some Noncommutative Theory
Appendix A. Relations
Appendix B. Zorn's Lemma
Bibliography
Index of Special Symbols
Index
