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Book synopsis

This book presents a graduate-level course on modern algebra. It can be used as a teaching book - owing to the copious exercises - and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan-Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic lessons on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that deals with a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.

Book details

Book category Books in English Mathematics & science Mathematics Algebra

• Full title: Algebra
• Author: Ernest Shult
• Language: English
• Binding: Paperback
• Number of pages: 539
• EAN: 9783319197333
• ISBN: 3319197339
• ID: 09296331
• Publisher: Springer, Berlin
• Weight: 849 g
• Dimensions: 30 × 155 × 235 mm
• Date of publishing: 23. July 2015

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