LEADER 04335nam 22006735 450 001 9910300247403321 005 20200703223345.0 010 $a3-319-19422-4 024 7 $a10.1007/978-3-319-19422-6 035 $a(CKB)3710000000532680 035 $a(EBL)4189307 035 $a(SSID)ssj0001597139 035 $a(PQKBManifestationID)16298305 035 $a(PQKBTitleCode)TC0001597139 035 $a(PQKBWorkID)14886704 035 $a(PQKB)10198814 035 $a(DE-He213)978-3-319-19422-6 035 $a(MiAaPQ)EBC4189307 035 $a(PPN)190851511 035 $a(EXLCZ)993710000000532680 100 $a20151212d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAbelian Groups /$fby László Fuchs 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (762 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a3-319-19421-6 320 $aIncludes bibliographical references and indexes. 327 $aFundamentals -- Direct Sums -- Direct Sums of Cyclic Groups -- Divisibility and Injectivity -- Purity and Basic Subgroups -- Algebraically Compact Groups -- Homomorphism Groups -- Tensor and Torsion Products -- Groups of Extensions and Cotorsion Groups -- Torsion Groups -- p-Groups with Elements of Infinite Height -- Torsion-free Groups -- Torsion-free Groups of Infinite Rank -- Butler Groups -- Mixed Groups -- Endomorphism Rings -- Automorphism groups -- Groups in Rings and in Fields. 330 $aWritten by one of the subject?s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah?s seminal work on the undecidability in ZFC of Whitehead?s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology, and homological algebra. An abundance of exercises are included to test the reader?s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject?s further development. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aGroup theory 606 $aCommutative algebra 606 $aCommutative rings 606 $aCategories (Mathematics) 606 $aAlgebra, Homological 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 615 0$aGroup theory. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aCategories (Mathematics) 615 0$aAlgebra, Homological. 615 14$aGroup Theory and Generalizations. 615 24$aCommutative Rings and Algebras. 615 24$aCategory Theory, Homological Algebra. 676 $a510 700 $aFuchs$b László$4aut$4http://id.loc.gov/vocabulary/relators/aut$041888 906 $aBOOK 912 $a9910300247403321 996 $aAbelian groups$9117768 997 $aUNINA