04093nam 22007455 450 991029978780332120200705234444.03-319-19734-710.1007/978-3-319-19734-0(CKB)3710000000454131(SSID)ssj0001558434(PQKBManifestationID)16183689(PQKBTitleCode)TC0001558434(PQKBWorkID)14819092(PQKB)10154268(DE-He213)978-3-319-19734-0(MiAaPQ)EBC6315039(MiAaPQ)EBC5587100(Au-PeEL)EBL5587100(OCoLC)1066188069(PPN)187685363(EXLCZ)99371000000045413120150714d2015 u| 0engurnn#008mamaatxtccrAlgebra A Teaching and Source Book /by Ernest Shult, David Surowski1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (XXII, 539 p. 6 illus.)Bibliographic Level Mode of Issuance: Monograph3-319-19733-9 Includes bibliographical references and index.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.Associative ringsRings (Algebra)Group theoryAlgebraField theory (Physics)Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Field Theory and Polynomialshttps://scigraph.springernature.com/ontologies/product-market-codes/M11051Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Associative rings.Rings (Algebra).Group theory.Algebra.Field theory (Physics).Associative Rings and Algebras.Group Theory and Generalizations.Field Theory and Polynomials.Algebra.512.9Shult Ernestauthttp://id.loc.gov/vocabulary/relators/aut51973Surowski Davidauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299787803321Algebra2523317UNINA