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13-01 Commutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.)

16-01 Associative rings and algebras -- Instructional exposition (textbooks, tutorial papers, etc.)

20-01 Group theory and generalizations -- Instructional exposition (textbooks, tutorial papers, etc.) En-ligne: MathSciNet

Location | Call Number | Status | Date Due |
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Salle R | 04068-01 / 12 DES (Browse Shelf) | Available |

This book is directed to "the student whose education in algebra may not have proceeded beyond college algebra''. It covers a great deal of what the reviewer would call "algebraic number-theory'' rather than "abstract algebra'': the systems of natural, integral, rational and real numbers, prime factorization and Euclid's algorithm in the system of integers, Diophantine equations, congruences, and quadratic residues. In the course of this work, such algebraic concepts as operation, isomorphism, embedding and homomorphism are defined and illustrated.

The book covers group theory as far as a proof that every finite Abelian group is a direct product of prime-power groups, a proof of Sylow's theorem on the existence of prime-power subgroups, and a statement (but no proof) of the Jordan-Hölder theorem.

The theory of rings and fields is covered as far as applications of Galois theory to cube-duplication and angle-trisection, and the study of finite fields.

The book ends with three chapters on linear algebra, starting with a definition of vector space, and going as far as the study of the Jordan normal form and a proof of the Cayley-Hamilton theorem.

Each chapter has its own bibliography. The book is well-supplied with routine exercises. There is a van der Waerden type map showing the interdependence of chapters (they are not far from being linearly ordered). (MathSciNet)

Bibliogr. Index

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