Abelian Groups, Rings, Modules, and Homological Algebra

Abelian Groups, Rings, Modules, and Homological Algebra

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About the book...In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the participants of these talks along with contributions from other veteran researchers who were unable to attend. These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors...H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group. OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visiting assistant professor in 1987. In 1988, he joined the Algebra research group at Auburn University.show more

Product details

  • Paperback | 360 pages
  • 152 x 230 x 28mm | 499.99g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 15 black & white illustrations
  • 1584885521
  • 9781584885528

Table of contents

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 B'EZOUT 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, Jorg 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 Pruferdomains Questions Appendix:Corrections to17 COVERS AND RELATIVE PURITY OVER COMMUTATIVE NOETHERIAN LOCAL RINGS, JR Garc'ia 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, Rudiger Gobel 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 ringsshow more