Title

Login

Join

Book's by David Surowski

Covers

List

Algebra

A Teaching and Source Book

By: Ernest Shult,David Surowski

Write a review Read reviews Take a Quiz Solve Book Puzzle

Algebra

A Teaching and Source Book

By: Ernest Shult,David Surowski

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.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

Solve jigsaw puzzle

Age

Page Count

551

Publisher

Springer

Published Date

ISBN 10

3319197347

ISBN 13

9783319197340

Algebra

A Teaching and Source Book

By: Ernest Shult,David Surowski

Write a review Read reviews Take a Quiz Solve Book Puzzle

Algebra

A Teaching and Source Book

By: Ernest Shult,David Surowski

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.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

Solve jigsaw puzzle

Age

Page Count

551

Publisher

Springer

Published Date

ISBN 10

3319197347

ISBN 13

9783319197340