Algebra

David Surowski

ISBN 10: 3319197339 / ISBN 13: 9783319197333

Published by Springer International Publishing Jul 2015, 2015

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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 courses 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 ideals in 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. 564 pp. Englisch.

Seller Inventory # 9783319197333

Bibliographic Details

• Title: Algebra
• Publisher: Springer International Publishing Jul 2015
• Publication Date: 2015
• Language: English
• ISBN 10: 3319197339
• ISBN 13: 9783319197333
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 31D millimeters 235 millimeters width by 155 millimeters height by 31 millimeters depth
• Weight: 844 grams

About this title

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 courses 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 ideals in 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.

About the Author

Ernest Shult studied finite groups with Michio Suzuki and held visiting fellowships at the University of Chicago and the Princeton Institute for Advanced Study in the 1960's. He continued to contribute to finite groups until he got interested in incidence geometry, In 1987-8 he received a US Scientist Award from the Alexander von Humboldt Foundation in Freiburg Germany.

David Surowski studied with Larry C. Grove and wrote numerous papers on the representation theory of groups with (B,N) pairs. Eventually his research came to include regular maps on surfaces. He was the recipient of many teaching awards and directed two summer institutes for young students of high ability. He died in March 2011.