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Algebra : A Teaching and Source Book / by Ernest Shult, David Surowski

1st ed. 2015.
出版者 Cham : Springer International Publishing : Imprint: Springer
出版年 2015
大きさ XXII, 539 p. 6 illus : online resource
著者標目 *Shult, Ernest author
Surowski, David author
SpringerLink (Online service)
件 名 LCSH:Associative rings
LCSH:Associative algebras
LCSH:Group theory
LCSH:Algebraic fields
LCSH:Polynomials
LCSH:Algebra
FREE:Associative Rings and Algebras
FREE:Group Theory and Generalizations
FREE:Field Theory and Polynomials
FREE:Algebra
一般注記 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
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
HTTP:URL=https://doi.org/10.1007/978-3-319-19734-0
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Springer eBooks 9783319197340
電子リソース
EB00208382

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データ種別 電子ブック
分 類 LCC:QA251.5
DC23:512.46
書誌ID 4000118611
ISBN 9783319197340

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