Direct Sum Decompositions of Torsion-Free Finite Rank Groups

ISBN: 9780367389321 出版年：2007 页码：339 Faticoni, Theodore G CRC Press

PREFACE NOTATION AND PRELIMINARY RESULTS Abelian Groups Associative Rings Finite Dimensional Q-Algebras Localization in Commutative Rings Local-Global Remainder Integrally Closed Rings Semi-Perfect Rings Exercise MOTIVATION BY EXAMPLE Some Well Behaved Direct Sums Some Badly Behaved Direct Sums Corner's Theorem Arnold-Lady-Murley Theorem Local Isomorphism Exercises Questions for Future Research LOCAL ISOMORPHISM IS ISOMORPHISM Integrally Closed Rings Conductor of an Rtffr Ring Local Correspondence Canonical Decomposition Arnold's Theorem Exercises Questions for Future Research COMMUTING ENGOMORPHISMS Nilpotent Sets Commutative Rtffr Rings E-Properties Square-Free Ranks Refinement and Square-Free Rank Hereditary Endomorphism Rings Exercises Questions for Future Research REFINEMENT REVISITED Counting Isomorphism Classes Integrally Closed Groups Exercises Questions for Future Research BAER SPLITTING PROPERTY Baer's Lemma Splitting of Exact Sequences G-Compressed Projectives Some Examples Exercises Questions for Future Research J-GROUPS, L- GROUPS, AND S- GROUPS Background on Ext Finite Projective Properties Finitely Projective Groups Finitely Faithful S-Groups Isomorphism versus Local Isomorphism Analytic Number Theory Eichler L-Groups Are J-Groups Exercises Questions for Future Research GABRIEL FILTERS Filters of Divisibility Idempotent Ideals Gabriel Filters on Rtffr Rings Gabriel Filters on QEnd(G) Exercises Questions for Future Research ENDOMORPHISM MODULES Additive Structures of Rings E-Properties Homological Dimensions Self-Injective Rings Exercises Questions for Future Research APPENDIX A: Pathological Direct Sums Nonunique Direct Sums APPENDIX B: ACD Groups Example by Corner APPENDIX C: Power Cancellation Failure of Power Cancellation APPENDIX D: Cancellation Failure of Cancellation APPENDIX E: Corner Rings and Modules Topological Preliminaries The Construction of G Endomorphisms of G APPENDIX F: Corner's Theorem Countable Endomorphism Rings APPENDIX G: Torsion Torsion-Free Groups E-Torsion Groups Self-Small Corner Modules APPENDIX H: E-Flat Groups Ubiquity Unfaithful Groups APPENDIX I: Zassenhaus and Butler Statement Proof APPENDIX J: Countable E-Rings Countable Torsion-Free E-Rings APPENDIX K: Dedekind E-Rings Number Theoretic Preliminaries Integrally Closed Rings BIBLIOGRAPHY INDEX