02997nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001600165072002300181082001500204100002800219245010100247264007500348300004400423336002600467337002600493338003600519347002400555505040300579520111900982650001702101650001302118650002302131650002102154650002802175650001802203650001702221650003602238650003802274650003402312650001302346700003002359710003402389773002002423776003602443856004802479978-3-319-19734-0DE-He21320180115171635.0cr nn 008mamaa150714s2015 gw | s |||| 0|eng d a97833191973407 a10.1007/978-3-319-19734-02doi 4aQA251.5 7aPBF2bicssc 7aMAT0020102bisacsh04a512.462231 aShult, Ernest.eauthor.10aAlgebrah[electronic resource] :bA Teaching and Source Book /cby Ernest Shult, David Surowski. 1aCham :bSpringer International Publishing :bImprint: Springer,c2015. aXXII, 539 p. 6 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 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. 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. 0aMathematics. 0aAlgebra. 0aAssociative rings. 0aRings (Algebra). 0aField theory (Physics). 0aGroup theory.14aMathematics.24aAssociative Rings and Algebras.24aGroup Theory and Generalizations.24aField Theory and Polynomials.24aAlgebra.1 aSurowski, David.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978331919733340uhttp://dx.doi.org/10.1007/978-3-319-19734-0