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



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Autore: Shult Ernest Visualizza persona
Titolo: Algebra : A Teaching and Source Book / / by Ernest Shult, David Surowski Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Edizione: 1st ed. 2015.
Descrizione fisica: 1 online resource (XXII, 539 p. 6 illus.)
Disciplina: 512.9
Soggetto topico: Associative rings
Rings (Algebra)
Group theory
Algebra
Field theory (Physics)
Associative Rings and Algebras
Group Theory and Generalizations
Field Theory and Polynomials
Persona (resp. second.): SurowskiDavid
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Algebra  Visualizza cluster
ISBN: 3-319-19734-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910299787803321
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