Algebra [[electronic resource] ] : A Teaching and Source Book / / by Ernest Shult, David Surowski
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| Autore: |
Shult Ernest
|
| Titolo: |
Algebra [[electronic resource] ] : A Teaching and Source Book / / by Ernest Shult, David Surowski
|
| 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 |
| ISBN: | 3-319-19734-7 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910299787803321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |