LEADER 03940nam 2200661Ia 450 001 9910463483903321 005 20210624212228.0 010 $a1-283-42903-9 010 $a9786613429032 010 $a3-11-021521-7 024 7 $a10.1515/9783110215212 035 $a(CKB)3360000000338765 035 $a(EBL)799388 035 $a(OCoLC)769190340 035 $a(SSID)ssj0000551992 035 $a(PQKBManifestationID)11360332 035 $a(PQKBTitleCode)TC0000551992 035 $a(PQKBWorkID)10538091 035 $a(PQKB)10655017 035 $a(MiAaPQ)EBC799388 035 $a(DE-B1597)36080 035 $a(OCoLC)979744861 035 $a(DE-B1597)9783110215212 035 $a(Au-PeEL)EBL799388 035 $a(CaPaEBR)ebr10515808 035 $a(CaONFJC)MIL342903 035 $a(EXLCZ)993360000000338765 100 $a20110627d2011 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aRelative homological algebra$hVolume 1$b[electronic resource] /$fEdgar E. Enochs, Overtoun M.G. Jenda 205 $a2nd rev. and extended ed. 210 $aBerlin ;$aBoston $cDe Gruyter$dc2011 215 $a1 online resource (376 p.) 225 1 $aDe Gruyter expositions in mathematics ;$v30 300 $aDescription based upon print version of record. 311 0 $a3-11-021520-9 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tPreface to the Second Edition --$tContents --$tChapter 1. Basic Concepts --$tChapter 2. Flat Modules, Chain Conditions and Prime Ideals --$tChapter 3. Injective and Flat Modules --$tChapter 4. Torsion Free Covering Modules --$tChapter 5. Covers --$tChapter 6. Envelopes --$tChapter 7. Covers, Envelopes, and Cotorsion Theories --$tChapter 8. Relative Homological Algebra and Balance --$tChapter 9. Iwanaga-Gorenstein and Cohen-Macaulay Rings and Their Modules --$tChapter 10. Gorenstein Modules --$tChapter 11. Gorenstein Covers and Envelopes --$tChapter 12. Balance over Gorenstein and Cohen-Macaulay Rings --$tBibliographical Notes --$tBibliography --$tIndex 330 $aThis is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following: Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3. Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader. Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published. The authors also have clarified some text throughout the book and updated the bibliography by adding new references. The book is also suitable for an introductory course in commutative and ordinary homological algebra. 410 0$aDe Gruyter expositions in mathematics ;$v30. 606 $aAlgebra, Homological 608 $aElectronic books. 615 0$aAlgebra, Homological. 676 $a512/.64 686 $aSK 260$2rvk 700 $aEnochs$b Edgar E$0725871 701 $aJenda$b Overtoun M. G$0725870 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910463483903321 996 $aRelative homological algebra$91424698 997 $aUNINA