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Description
Elements of Abstract AlgebraThis concise, readable, college level 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
This concise, readable, college-level 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 Jordan-Holder 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.
Binding Type: Paperback
Publisher: Dover Publications
Published: 10/01/1984
ISBN: 9780486647258
Pages: 224
Weight: 0.60lbs
Size: 8.40h x 5.50w x 0.50d
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Reviewed in the United States on April 22, 2025
★★★★★ 5
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★★★★★ 5
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Size: 13 Little Kid, Color: Lavender/Multi, Size: 13 Little Kid, Color: Lavender/Multi
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Reviewed in the United States on May 9, 2025
★★★★★ 5
Cute and comfu
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Reviewed in the United States on April 5, 2026
★★★★★ 5
Great durability & washablity.
Size: 4 Big Kid, Color: Lavender/Multi
These Skechers slip on shoes are perfect for kiddos! I've probably bought +20 pairs between my 3 daughters over the past 3-4 years. The shoes are comfortable, durable, last until the kids outgrow them, and best of all are easy to wash in my clothes washer. Definitely a great value. They come in so many different colors and styles that my kids easily find a pair that satisfy their personal tastes.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on April 22, 2025