Title
Elements of Abstract Algebra (Dover Books on Mathematics),Used
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This concise, readable, collegelevel text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the JordanHolder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory) reviews linear algebra and introduces fields as a prelude to Galois theory. In addition there is a full discussion of the constructibility of regular polygons. Chapter IV (Galois Theory) gives a thorough treatment of this classical topic, including a detailed presentation of the solvability of equations in radicals that actually includes solutions of equations of degree 3 and 4 a feature omitted from all texts of the last 40 years. Chapter V (Ring Theory) contains basic information about rings and unique factorization to set the stage for classical ideal theory. Chapter VI (Classical Ideal Theory) ends with an elementary proof of the Fundamental Theorem of Algebraic Number Theory for the special case of Galois extensions of the rational field, a result which brings together all the major themes of the book.The writing is clear and careful throughout, and includes many historical notes. Mathematical proof is emphasized. The text comprises 198 articles ranging in length from a paragraph to a page or two, pitched at a level that encourages careful reading. Most articles are accompanied by exercises, varying in level from the simple to the difficult.
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- Q: What is the main focus of 'Elements of Abstract Algebra'? A: The book primarily focuses on basic abstract algebra, covering key areas such as group theory, Galois theory, and classical ideal theory in depth.
- Q: Who is the author of this book? A: The author of 'Elements of Abstract Algebra' is Allan Clark.
- Q: How many pages does the book have? A: The book consists of 224 pages.
- Q: What edition of the book is available? A: This is the 47.3 edition of 'Elements of Abstract Algebra'.
- Q: What is the publication date of this book? A: The book was published on October 1, 1984.
- Q: Is this book suitable for beginners in abstract algebra? A: The text is college-level and requires some prior knowledge of mathematics, making it more suitable for those with a basic understanding of algebra.
- Q: What topics are covered in Chapter II of the book? A: Chapter II focuses on group theory, providing a rigorous introduction and covering essential results for Galois theory.
- Q: Are there exercises included in the book? A: Yes, most of the 198 articles in the book are accompanied by exercises that range from simple to difficult.
- Q: Does the book include historical notes? A: Yes, the writing includes many historical notes alongside the mathematical content.
- Q: What type of binding does this book have? A: The book is available in paperback binding.