Introduction to Modern Abstract Algebra by David M. Burton
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Introduction to Modern Abstract Algebra written by
David M. Burton . Published by
Addison-Wesley , Year: 1967, ISBN: 0201007223,9780201007220.
This book has been written with the intention of providing an introduction to model'll aht:!t.ract algebra for mathematics major8. The r('.ader is not presumed at thc Outllct to possess any previout:! knowledge of the concepts of modem algebra. Accordingly, our beginuing is somewhat elementary, with the exposition in the earlier sections proceeding at a leisurely pace; much of this early material may be covered rapidly on a first reading. An attempt. has been made to keep the book as self-contained as possible. To smooth the path for the unexperienced reader, the fir8t chapter is devoted to a review of the basic facts concerning sets, functions and number theory; it also serves as a suitable vehicle for introducing some of the notation and terminology used subsequently.
A cursory examination of the table of contents will reveal few surprises; the topics chosen for discussion in COUr8es at this level are fairly standard. However, our aim has been to give a presentation which is logically developed, precise, and in keeping with the spirit of the times. Thus, set notation is employed throughout, and the distinction is maintained between algebraic systems as ordered pair8 or triples and their underlying sets of elements. Guided by the principII! thnt 0. st(~l"ly diet. of definitions and cxullIples SOOIl 1)(~c()llIel'l unpalatable, our eiTOl-ts are directed towards establishing the most important and fruitful results of the subject in a formal, rigorous fashion. The chapter on groups, fOl' example, culminates in a proof of the classic Sylow Theorems, while ring and ideal theory are developed to the point of obtaining the Stoile Representation Theorem for Boolean rings. Ell route, it is hoped that the, reader will gain an appreciation of precise mathematical thought and t.he current standards of rigor.
Introduction to Modern Abstract Algebra written by
David M. Burton
cover the following topics.
1. Preliminary Notion
2. Group Theory
3. Ring Theory
4. Vector Spece
Index
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