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[null,"1.","Record Nr.",null,"UNINA9910299787803321"]
[null,null,"Autore",null,"Shult Ernest"]
[null,null,"Titolo",null,"Algebra : A Teaching and Source Book / / by Ernest Shult, David Surowski"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015"]
[null,null,"ISBN",null,"3-319-19734-7"]
[null,null,"Edizione",null,"[1st ed. 2015.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XXII, 539 p. 6 illus.)"]
[null,null,"Disciplina",null,"512.9"]
[null,null,"Soggetti",null,"Associative rings"]
[{"$nulls":4},"Rings (Algebra)"]
[{"$nulls":4},"Group theory"]
[{"$nulls":4},"Algebra"]
[{"$nulls":4},"Field theory (Physics)"]
[{"$nulls":4},"Associative Rings and Algebras"]
[{"$nulls":4},"Group Theory and Generalizations"]
[{"$nulls":4},"Field Theory and Polynomials"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Basics -- Basic Combinatorial Principles of Algebra -- Review of Elementary Group Properties -- Permutation Groups and Group Actions -- Normal Structure of Groups -- Generation in Groups -- Elementary Properties of Rings -- Elementary properties of Modules -- The Arithmetic of Integral Domains -- Principal Ideal Domains and Their Modules -- Theory of Fields -- Semiprime Rings -- Tensor Products."]
[null,null,null,"Sommario/riassunto","This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results "]
[{"$nulls":4},"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."]