Abelian Groups, Rings, Modules, and Homological Algebra (Hardcover)

GENERALIZING WARFIELD'S HOM AND TENSOR RELATIONS, Ulrich Albrecht and Pat GoetersIntroduction1Self-Small ModulesProjectivity PropertiesThe Class MADomains Which Support Warfield's ResultsReplicating Duality for DomainsDuality and Infinite ProductsMixed Groups HOW FAR IS AN HFD FROM A UFD?, David F Anderson and Elizabeth V MclaughlinIntroduction3R/LocalizationQuestions A COUNTER EXAMPLE FOR A QUESTION ON PSEUDO-VALUATION RINGS, Ayman BadawiIntroductionCounter exampleCO-LOCAL SUBGROUPS OF ABELIAN GROUPS, Joshua Buckner and Manfred DugasIntroductionBasic PropertiesCotorsion-free groups as co-local subgroups PARTITION BASES AND B1- GROUPS, Immacolata Caruso, Clorinda De Vivo and ClaudiaMetelliIntroductionPreliminaries Partition bases Direct Summands The Domain of C;D Indecomposable summandsExamples ASSOCIATED PRIMES OF THE LOCAL COHOMOLOGY MODULES, Mohammad T Dibaei and Siamak YassemiIntroductionGeneral caseSpecial caseGeneralized local cohomologyON INVERSE LIMITS OF B´EZOUT DOMAINS, David E Dobbs and Marco FontanaIntroductionResults AN ELEMENTARY PROOF OF GROTHENDIECK'S THEOREM, E Enochs, S Estrada and B TorrecillasIntroductionThe main theorem Grothendieck's Theorem GORENSTEIN HOMOLOGICAL ALGEBRA, Edgar E Enochs and Overtoun MG JendaIntroductionTate Homology and Cohomology Auslander and Gorenstein Rings The Kaplansky ProgramIwanaga-Gorenstein RingsGorenstein Homological Algebra Generalized Tate Homology and CohomologyThe Avramov-Martsinkovsky ProgramGorenstein Flat Modules Salce's Cotorsion TheoriesOther Possibilities MODULES AND POINT SET TOPOLOGICAL SPACES, Theodore G FaticoniThe DiagramSelf-small and Self-slender Modules The Construction FunctionThe Greek MapsCoherent Modules and ComplexesComplete Setsof InvariantsUnique DecompositionsHomological Dimensions Miscellaneous INJECTIVEMODULES AND PRIME IDEALS OF UNIVERSAL ENVELOPING ALGEBRAS, J¨org FeldvossInjective Modules and Prime IdealsInjectiveHulls Locally Finite Submodules of the Coregular Module Minimal Injective Resolutions COMMUTATIVE IDEAL THEORY WITHOUT FINITENESS CONDITIONS, Laszlo Fuchs, William Heinzer and Bruce OlberdingIntroductionThe structure of Q-irreducible ideals Completely Q-irreducible and m-canonical idealsQ-irreducibility and injective modulesIrredundant decompositions and semi-artinian modules Pr¨uferdomains Questions Appendix:Corrections to17COVERS AND RELATIVE PURITY OVER COMMUTATIVE NOETHERIAN LOCAL RINGS, JR Garc´ia Rozas, L Oyonarte and B TorrecillasPreliminariestI -closed modulesRelative purity over local ringsRelative purity over regular local ringsTORSIONLESS LINEARLY COMPACT MODULES, R¨udiger G¨obel and Saharon ShelahIntroductionProof of the Theorem BIG INDECOMPOSABLE MIXED MODULES OVER HYPERSURFACE SINGULARITIES, Wolfgang Hassler and Roger WiegandIntroductionBimodules Extensions Syzygies and double branched covers Finding a suitable finite-length moduleThe main application EVERY ENDOMORPHISM OF A LOCAL WARFIELD MODULE IS THE SUM OF TWO AUTOMORPHISMS, Paul Hill, Charles Megibben and William UlleryIntroductionThe Key LemmaProof of the Main TheoremWAKAMATSU TILTING MODULES, U-DOMINANT DIMENSION AND K-GORENSTEIN MODULES, Zhaoyong HuangIntroduction and main results Wakamatsu tilting modulesThe proof of main results Exactness of the double dual A generalization of k-Gorenstein modulesG-SEPARATED COVERS, Lawrence S Levy and Jan TrlifajIntroductionG-coversG-separated covers The Dedekind-likecaseOpenProblemsTHE COTORSION DIMENSION OF MODULES AND RINGS, Lixin Mao and Nanqing DingIntroductionGeneral results Cotorsion dimension under change of ringsApplications incommutative ringsMAXIMAL SUBRINGS OF HOMOGENEOUS FUNCTIONS, C J MaxsonIntroductionThe Case of Torsion GroupsThe Case of Torsion-Free Groups Subrings of M0(A)ISOTYPE SEPARABLE SUBGROUPS OF MIXED ABELIAN GROUPS, Charles Megibben and William UlleryIntroductionSubgroups with _-covers of almost balanced pure subgroupsIntersection closure of global Warfield groupsIsotype separable subgroups of globalWarfield groupsNOTE ON THE GENERALIZED DERIVATION TOWER THEOREM FOR LIE ALGEBRAS, Toukaiddine Petit and Fred Van OystaeyenIntroductionG-Decomposition Derivation tower of Lie algebras: case with trivialc enter The Derivation tower of Lie algebras: general caseQUOTIENT DIVISIBLE GROUPS, !-GROUPS, AND AN EXAMPLE OF FUCHS, J D ReidIntroductionOn w-groups Three RemarksParameters Main ResultsEndomorphismsWHEN ARE ALMOST PERFECT DOMAINS NOETHERIAN?, Luigi SalceIntroductionKnown results on the Noetherian condition A characterization of Noetherian almost perfect domainsE-closed domains PURE INVARIANCE IN TORSION-FREE ABELIAN GROUPS, Phill SchultzIntroductionPure fully invariant subgroups Traces and kernels of cd groupsCOMPRESSIBLE AND RELATED MODULES, Patrick F SmithIntroductionPrime and compressible modules Monoform modulesNonsingular modules Fully bounded rings