Algebra [electronic resource] : a teaching and source book / Ernest Shult, David Surowski.

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Algebra [electronic resource] : a teaching and source book / Ernest Shult, David Surowski.

9783319197340 electronic book
3319197347 electronic book
9783319197333

Cham : Springer, 2015.

English

1 online resource (xxii, 539 pages) : illustrations

10.1007/978-3-319-19734-0 doi

QA152.3

512

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed July 21, 2015).

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