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010   $a3-319-19734-7
024 7 $a10.1007/978-3-319-19734-0
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035   $a(DE-He213)978-3-319-19734-0
035   $a(MiAaPQ)EBC6315039
035   $a(MiAaPQ)EBC5587100
035   $a(Au-PeEL)EBL5587100
035   $a(OCoLC)1066188069
035   $a(PPN)187685363
035   $a(EXLCZ)993710000000454131
100   $a20150714d2015      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aAlgebra $eA Teaching and Source Book /$fby Ernest Shult, David Surowski
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (XXII, 539 p. 6 illus.)
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-19733-9 
320   $aIncludes bibliographical references and index.
327   $aBasics -- 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.
330   $aThis 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.
606   $aAssociative rings
606   $aRings (Algebra)
606   $aGroup theory
606   $aAlgebra
606   $aField theory (Physics)
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051
606   $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000
615  0$aAssociative rings.
615  0$aRings (Algebra).
615  0$aGroup theory.
615  0$aAlgebra.
615  0$aField theory (Physics).
615 14$aAssociative Rings and Algebras.
615 24$aGroup Theory and Generalizations.
615 24$aField Theory and Polynomials.
615 24$aAlgebra.
676   $a512.9
700   $aShult$b Ernest$4aut$4http://id.loc.gov/vocabulary/relators/aut$051973
702   $aSurowski$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299787803321
996   $aAlgebra$92523317
997   $aUNINA