Algebra : a teaching and source book /
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 conditi...
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham :
Springer,
[2015]
|
| Subjects: |
| Summary: | 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. |
|---|---|
| Physical Description: | xxii, 539 pages : illustrations ; 24 cm |
| Audience: | Graduates. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9783319197333 3319197339 |