ENGLISH

Algebra: A Teaching and Source Book

By Ernest Shult , David Surowski (auth.)

Book information

Publisher
Springer International Publishing
Year
2015
ISBN
978-3-319-19733-3, 978-3-319-19734-0
DOI
10.1007/978-3-319-19734-0
Language
english
Format
PDF
Filesize
5 MB (5267181 bytes)
Edition
1
Pages
XXII, 539\551
Topic
Mathematics Algebra
Time added
2015-11-25 16:51:03
Associative Rings and Algebras; Group Theory and G

Description

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.

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