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

• Autore: Shult Ernest
• 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