| eBook ISBN: | 978-1-61444-008-6 |
| Product Code: | CAR/8.E |
| List Price: | $45.00 |
| MAA Member Price: | $33.75 |
| AMS Member Price: | $33.75 |
| eBook ISBN: | 978-1-61444-008-6 |
| Product Code: | CAR/8.E |
| List Price: | $45.00 |
| MAA Member Price: | $33.75 |
| AMS Member Price: | $33.75 |
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Book DetailsThe Carus Mathematical MonographsVolume: 8; 1948; 216 pp
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, as far as formal technique is concerned, little more than the elements of algebra are presupposed.
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Table of Contents
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Chapters
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Chapter I. Definitions and fundamental properties
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Chapter II. Polynomial rings
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Chapter III. Ideals and homomorphisms
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Chapter IV. Some imbedding theorems
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Chapter V. Prime ideals in commutative rings
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Chapter VI. Direct and subdirect sums
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Chapter VII. Boolean rings and some generalizations
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Chapter VIII. Rings of matrices
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Chapter IX. Further theory of ideals in commutative rings
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Additional Material
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Reviews
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The book presupposes no previous training in algebra (except that in certain parts determinants are used). Because of the clarity with which it is written and because of the consistent use of simple examples to motivate the introduction of new ideas, it can be read without difficulty by those who are new to the subject.
I. S. Cohen, Mathematical Reviews
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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, as far as formal technique is concerned, little more than the elements of algebra are presupposed.
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Chapters
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Chapter I. Definitions and fundamental properties
-
Chapter II. Polynomial rings
-
Chapter III. Ideals and homomorphisms
-
Chapter IV. Some imbedding theorems
-
Chapter V. Prime ideals in commutative rings
-
Chapter VI. Direct and subdirect sums
-
Chapter VII. Boolean rings and some generalizations
-
Chapter VIII. Rings of matrices
-
Chapter IX. Further theory of ideals in commutative rings
-
The book presupposes no previous training in algebra (except that in certain parts determinants are used). Because of the clarity with which it is written and because of the consistent use of simple examples to motivate the introduction of new ideas, it can be read without difficulty by those who are new to the subject.
I. S. Cohen, Mathematical Reviews
