Abelian Group Theory: Proceedings Of The Conference Held At The University Of Hawaii, Honolulu, Usa, December 28, 1982 - January 4, 1983 (lecture Notes In Mathematics) (french And English Edition)

A conference on Abelian Group Theory was held at the Manoa Campus of the University of Hawaii from December 28, 1982 to January 4, 1983. It was probably the best attended conference on Abelian Group Theory to date with 55 participants from allover the world and the busiest one with 49 talks. A special feature were general interest lectures by Hyman Bass, Columbia University, on "Non-linear Algebra", and by Claus Michael Ringel, Uni versiUit Bielefeld, on "Representations of Algebras". The Conference offered surveys by Laszlo Fuchs, Tulane University, on "Torsion Modules over Valuation Rings", Fred Richman, New Mexico State University, on "Mixed Groups", Paul Eklof, University of California at Irvine, on "Set Theory and Structure Theorems", Rudiger Gobel, Un:i:versitat Essen on "Endomorphism Rings", and Lee Lady, University of Hawaii, on "Torsion Free Groups of Finite Rank". The research reports attested to lively activity in the traditional and in new areas of inquiry within and around Abelian Group Theory. The best represented groups were those of finite rank without torsion, a field employing increasingly sophisticated tools from ring theory and algebraic number theory. The use of set theoretic methods continues to flourish after the pioneering work of Saharon Shelah in the 1970s, and is delivering impressive results. This volume contains the papers of the participants df the C- ferencean6 a number of additional articles of others who could not or did not corne A seminar on splitting rings for torsion free modules over dedekind domains....Pages 1-48 Realizing algebraic number fields....Pages 49-96 Pure subgroups of finite rank completely decomposable groups II....Pages 97-143 Projective and injective classes of completely decomposable groups....Pages 144-163 Extensions of Butler groups....Pages 164-170 Butler groups of infinite rank....Pages 171-189 Abelian groups cyclic over their endomorphism rings....Pages 190-203 Abelian groups which are uniserial as modules over their endomorphism rings....Pages 204-208 Endomorphism rings and A-projective torsion-free abelian groups....Pages 209-227 Type graph....Pages 228-252 On type-related properties of torsionfree abelian groups....Pages 253-267 On strongly balanced subgroups of separable torsion-free abelian groups....Pages 268-274 Set theory and structure theorems....Pages 275-284 Proper forcing and abelian groups....Pages 285-303 Methods of set theory and the abundance of separable abelian p-groups....Pages 304-319 On endomorphism rings of ω 1 -separable primary groups....Pages 320-339 Endomorphism rings of abelian groups....Pages 340-353 On the existence of very decomposable abelian groups....Pages 354-357 Sur Des Decompositions Directs Paradoxales De Groupes Abeliens Sans Torsion....Pages 358-361 On κ-products modulo μ-products....Pages 362-370 A note on subgroups of Z N ....Pages 371-374 Slenderness in abelian categories....Pages 375-383 Endomorphism rings of abelian p-groups....Pages 384-399 Endomorphism algebras of torsion modules II....Pages 400-411 On the existence of large mixed modules....Pages 412-424 Countable countably — Indecomposable abelian groups, n-decomposable for any finite n....Pages 425-435 Characterizations of quasi-splitting abelian groups....Pages 436-444 Mixed groups....Pages 445-470 Finite valuated p-groups....Pages 471-507 A basis thforem for subgroups of finite abelian groups....Pages 508-512 On the congruence of subgroups of totally projectives....Pages 513-518 Pure dense subgroups that are isomorphic to every pure subgroup supported by their socles....Pages 519-522 p ω+n -projective abelian p-groups having big direct sum of cyclic summands....Pages 523-533 Extensions of torsion complete groups....Pages 534-547 Abelian groups in which every Γ-isotype subgroup is an intersection of Γ′-isotype subgroups....Pages 548-555 Straight bases of abelian p-groups....Pages 556-561 Completions via duality....Pages 562-568 Completions of valuated abelian groups....Pages 569-581 Topologies Linéaires Minimales Sur Un Groupe Abélien....Pages 582-588 On projective dimensions of modules over valuation domains....Pages 589-598 Exterior powers and torsion-free modules over almost maximal valuation domains....Pages 599-606 On torsion-free modules of rank 2 over an almost maximal valuation domain....Pages 607-616 A generalization of a Prufer-Kaplansky theorem....Pages 617-629 Closed submodules....Pages 630-638 On torsion abelian groups like modules....Pages 639-653 On modules and radicals....Pages 654-659 Preradicals induced by homomorphisms....Pages 660-670 Singly generated socles and radicals....Pages 671-684 On a certain isomorphism....Pages 685-695 Abelian group theory and p-maps....Pages 696-710 A remark on integral duality....Pages 711-719 Augmentation terminals of finite Abelian groups....Pages 720-733 Homological transfer from finitely presented to infinite modules....Pages 734-761 Automorphisms of polynomial rings....Pages 762-771