Rings and Ideals

Neal H. McCoy

doi:10.5948/9781614440086

The MAA is pleased to re-issue the early Carus Mathematical Monographs in ebook and print-on-demand formats. Readers with an interest in the history of the undergraduate curriculum or the history of a particular field will be rewarded by study of these very clear and approachable little volumes. This monograph presents an introduction to that branch of abstract algebra having to do with the theory of rings, with some emphasis on the role of ideals in the theory. Except for a knowledge of certain fundamental theorems about determinants which is assumed in Chapter VIII, and at one point in Chapter VII, the book is almost entirely self-contained. Of course, the reader must have a certain amount of 'mathematical maturity' in order to understand the illustrative examples, and also to grasp the significance of the abstract approach. However, in so far as formal technique is concerned, little more than the elements of algebra are presupposed.

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Rings and Ideals

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Contents

Frontmatter
pp i-vi

PREFACE
pp vii-x

Contents
pp xi-xii

CHAPTER I - Definitions and Fundamental Properties
pp 1-30

CHAPTER II - Polynomial Rings
pp 31-51

CHAPTER III - Ideals and Homomorphisms
pp 52-82

CHAPTER IV - Some Imbedding Theorems
pp 83-95

CHAPTER V - Prime Ideals in Commutative Rings
pp 96-113

CHAPTER VI - Direct and Subdirect Sums
pp 114-137

CHAPTER VII - Boolean Rings and Some Generalizations
pp 138-149

CHAPTER VIII - Rings of Matrices
pp 150-179

CHAPTER IX - Further Theory of Ideals in Commutative Rings
pp 180-209

Bibliography
pp 210-214

Index
pp 215-216

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