Algebra A Teaching and Source Book /
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 conditi...
| Published in: | Springer eBooks |
|---|---|
| Main Authors: | , |
| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1007/978-3-319-19734-0 Перейти в каталог НБ ТГУ |
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| 100 | 1 | |a Shult, Ernest. |e author. |9 466847 | |
| 245 | 1 | 0 | |a Algebra |h electronic resource |b A Teaching and Source Book / |c by Ernest Shult, David Surowski. |
| 260 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. |9 742221 | ||
| 300 | |a XXII, 539 p. 6 illus. |b online resource. | ||
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| 505 | 0 | |a Basics -- Basic Combinatorial Principles of Algebra -- Review of Elementary Group Properties -- Permutation Groups and Group Actions -- Normal Structure of Groups -- Generation in Groups -- Elementary Properties of Rings -- Elementary properties of Modules -- The Arithmetic of Integral Domains -- Principal Ideal Domains and Their Modules -- Theory of Fields -- Semiprime Rings -- Tensor Products. | |
| 520 | |a 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. | ||
| 650 | 0 | |a mathematics. |9 566183 | |
| 650 | 0 | |a Algebra. |9 281363 | |
| 650 | 0 | |a Associative rings. |9 205882 | |
| 650 | 0 | |a Rings (Algebra). |9 460211 | |
| 650 | 0 | |a Field theory (Physics). |9 303209 | |
| 650 | 0 | |a Group theory. |9 303360 | |
| 650 | 1 | 4 | |a Mathematics. |9 566184 |
| 650 | 2 | 4 | |a Associative Rings and Algebras. |9 306398 |
| 650 | 2 | 4 | |a Group Theory and Generalizations. |9 303362 |
| 650 | 2 | 4 | |a Field Theory and Polynomials. |9 303211 |
| 650 | 2 | 4 | |a Algebra. |9 281363 |
| 700 | 1 | |a Surowski, David. |e author. |9 466848 | |
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| 856 | |y Перейти в каталог НБ ТГУ |u https://koha.lib.tsu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=414795 | ||
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