A First Course in Rings and Ideals

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. 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 [by] David M. Burton. Bibliography: P. 300-302.