An Introductory Course in Commutative Algebra (Oxford Science Publications) - Brossura

Chatters, A. W.

Brossura

ISBN 10: 0198501447 ISBN 13: 9780198501442

Casa editrice: Oxford University Press, 1998

Riassunto

This book aims to be a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. It combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields which has important uses in other branches of science. Topics covered include rings and Euclidean rings, the four-squares theorem, fields and field extensions, finite cyclic groups, and finite fields. The material covered in this book prepares the way for the further study of abstract algebra, but it could also form the basis of an entire course.

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Recensione

Immaculately organised, the text glides seamlessly from the concrete to the abstrat; it is carefully written without being pedantic and all of the right motivational and cautinoary noises are made as intuition and feel for each new concept is developed.

Contenuti

• 1: Rings
• 2: Euclidean rings
• 3: Highest common factor
• 4: The four-squares theorem
• 5: Fields and polynomials
• 6: Unique factorization domains
• 7: Field of quotients of an integral domain
• 8: Factorization of polynomials
• 9: Fields and field extensions
• 10: Finite cyclic groups and finite fields
• 11: Algebraic numbers
• 12: Ruler and Compass constructions
• 13: Homomorphisms, ideals and factor rings
• 14: Principal ideal domains and a method for constructing fields
• 15: Finite fields
• Solutions to selected exercises
• References

Dettagli dell?edizione

• Editore: Oxford University Press
• Data di pubblicazione: 1998
• ISBN 10: 0198501447
• ISBN 13: 9780198501442
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 160
• Contatto del produttore: non disponibile