Abelian groups, rings, modules, and homological algebra Book

GENERALIZING WARFIELD'S HOM AND TENSOR RELATIONS, Ulrich Albrecht and Pat Goeters Introduction1
Self-Small Modules Projectivity Properties The Class MA Domains Which Support Warfield's Results Replicating Duality for Domains Duality and Infinite Products Mixed Groups

HOW FAR IS AN HFD FROM A UFD?, David F Anderson and Elizabeth V Mclaughlin Introduction
3R/
Localization Questions

A COUNTER EXAMPLE FOR A QUESTION ON PSEUDO-VALUATION RINGS, Ayman Badawi Introduction Counter example

CO-LOCAL SUBGROUPS OF ABELIAN GROUPS, Joshua Buckner and Manfred Dugas Introduction Basic Properties Cotorsion-free groups as co-local subgroups

PARTITION BASES AND B1- GROUPS, Immacolata Caruso, Clorinda De Vivo and ClaudiaMetelli Introduction Preliminaries Partition bases Direct Summands The Domain of C;D Indecomposable summands Examples

ASSOCIATED PRIMES OF THE LOCAL COHOMOLOGY MODULES, Mohammad T Dibaei and Siamak Yassemi Introduction General case Special case Generalized local cohomology

ON INVERSE LIMITS OF BEZOUT DOMAINS, David E Dobbs and Marco Fontana Introduction Results

AN ELEMENTARY PROOF OF GROTHENDIECK'S THEOREM, E Enochs, S Estrada and B Torrecillas Introduction The main theorem Grothendieck's Theorem

GORENSTEIN HOMOLOGICAL ALGEBRA, Edgar E Enochs and Overtoun MG Jenda Introduction Tate Homology and Cohomology Auslander and Gorenstein Rings The Kaplansky Program Iwanaga-Gorenstein Rings Gorenstein Homological Algebra Generalized Tate Homology and Cohomology The Avramov-Martsinkovsky Program Gorenstein Flat Modules Salce's Cotorsion Theories Other Possibilities

MODULES AND POINT SET TOPOLOGICAL SPACES, Theodore G Faticoni The Diagram Self-small and Self-slender Modules The Construction Function The Greek Maps Coherent Modules and Complexes Complete Setsof Invariants Unique Decompositions Homological Dimensions Miscellaneous

INJECTIVEMODULES AND PRIME IDEALS OF UNIVERSAL ENVELOPING ALGEBRAS, J¨org Feldvoss Injective Modules and Prime Ideals InjectiveHulls Locally Finite Submodules of the Coregular Module Minimal Injective Resolutions

COMMUTATIVE IDEAL THEORY WITHOUT FINITENESS CONDITIONS, Laszlo Fuchs, William Heinzer and Bruce Olberding Introduction The structure of Q-irreducible ideals Completely Q-irreducible and m-canonical ideals Q-irreducibility and injective modules Irredundant decompositions and semi-artinian modules Pr¨uferdomains Questions Appendix:Corrections to17

COVERS AND RELATIVE PURITY OVER COMMUTATIVE NOETHERIAN LOCAL RINGS, JR García Rozas, L Oyonarte and B Torrecillas Preliminaries tI -closed modules Relative purity over local rings Relative purity over regular local rings

TORSIONLESS LINEARLY COMPACT MODULES, R¨udiger G¨obel and Saharon Shelah Introduction Proof of the Theorem

BIG INDECOMPOSABLE MIXED MODULES OVER HYPERSURFACE SINGULARITIES, Wolfgang Hassler and Roger Wiegand Introduction Bimodules Extensions Syzygies and double branched covers Finding a suitable finite-length module The main application

EVERY ENDOMORPHISM OF A LOCAL WARFIELD MODULE IS THE SUM OF TWO AUTOMORPHISMS, Paul Hill, Charles Megibben and William Ullery Introduction The Key Lemma Proof of the Main Theorem

WAKAMATSU TILTING MODULES, U-DOMINANT DIMENSION AND K-GORENSTEIN MODULES, Zhaoyong Huang Introduction and main results Wakamatsu tilting modules The proof of main results Exactness of the double dual A generalization of k-Gorenstein modules

G-SEPARATED COVERS, Lawrence S Levy and Jan Trlifaj Introduction G-covers G-separated covers The Dedekind-likecase

OpenProblems THE COTORSION DIMENSION OF MODULES AND RINGS, Lixin Mao and Nanqing Ding Introduction General results Cotorsion dimension under change of rings Applications incommutative rings

MAXIMAL SUBRINGS OF HOMOGENEOUS FUNCTIONS, C J Maxson Introduction The Case of Torsion Groups The Case of Torsion-Free Groups Subrings of M0(A)

ISOTYPE SEPARABLE SUBGROUPS OF MIXED ABELIAN GROUPS, Charles Megibben and William Ullery Introduction Subgroups with _-covers of almost balanced pure subgroups Intersection closure of global Warfield groups Isotype separable subgroups of globalWarfield groups

NOTE ON THE GENERALIZED DERIVATION TOWER THEOREM FOR LIE ALGEBRAS, Toukaiddine Petit and Fred Van Oystaeyen Introduction G-Decomposition Derivation tower of Lie algebras: case with trivialc enter The Derivation tower of Lie algebras: general case

QUOTIENT DIVISIBLE GROUPS, !-GROUPS, AND AN EXAMPLE OF FUCHS, J D Reid Introduction On w-groups Three Remarks Parameters Main Results Endomorphisms

WHEN ARE ALMOST PERFECT DOMAINS NOETHERIAN?, Luigi Salce Introduction Known results on the Noetherian condition A characterization of Noetherian almost perfect domains E-closed domains

PURE INVARIANCE IN TORSION-FREE ABELIAN GROUPS, Phill Schultz Introduction Pure fully invariant subgroups Traces and kernels of cd groups

COMPRESSIBLE AND RELATED MODULES, Patrick F Smith Introduction Prime and compressible modules Monoform modules Nonsingular modules Fully bounded rings