Hidden Bibliographic Details
| Other authors / contributors: | Surowski, David, 1949- author.
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| ISBN: | 9783319197340
3319197347
3319197339
9783319197333
9783319197333
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| Digital file characteristics: | text file PDF
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| Notes: | Includes bibliographical references and index.
Online resource; title from PDF title page (SpringerLink, viewed July 21, 2015).
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| Summary: | 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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| Other form: | Printed edition: 9783319197333
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| Standard no.: | 10.1007/978-3-319-19734-0
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