Algebra - A Teaching and Source Book (Paperback, 1st ed. 2015)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Release date:	July 2015
First published:	2015
Authors:	Ernest Shult • David Surowski
Dimensions:	235 x 155 x 29mm (L x W x T)
Format:	Paperback
Pages:	539
Edition:	1st ed. 2015
ISBN-13:	978-3-319-19733-3
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Promotions
LSN:	3-319-19733-9
Barcode:	9783319197333

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