Erschienen: 23.07.2015 Abbildung von Shult / Surowski | Algebra | 1. Auflage | 2015 | beck-shop.de

Shult / Surowski

Algebra

A Teaching and Source Book

Buch. Softcover

1st ed. 2015. 2015

xxii, 539 S. 6 s/w-Abbildungen, Bibliographien.

In englischer Sprache

Springer. ISBN 978-3-319-19733-3

Format (B x L): 15,5 x 23,5 cm

Gewicht: 854 g

Produktbeschreibung

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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