Approximations and endomorphism algebras of modules: 2 Predictions
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| Format: | Book |
| Language: | English |
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Berlin [u.a.]
de Gruyter
2012
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| Edition: | 2., rev. and extended ed. |
| Series: | De Gruyter expositions in mathematics
41,2 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV S., S. 462 - 972 graph. Darst. |
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| 245 | 1 | 0 | |a Approximations and endomorphism algebras of modules |n 2 |p Predictions |c Rüdiger Göbel ; Jan Trlifaj |
| 250 | |a 2., rev. and extended ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2012 | |
| 300 | |a XXIV S., S. 462 - 972 |b graph. Darst. | ||
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| 490 | 1 | |a De Gruyter expositions in mathematics |v 41,2 | |
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| adam_text | IMAGE 1
CONTENTS
VOLUME 2
INTRODUCTION XV
LIST OF SYMBOLS XXI
IV PREDICTION PRINCIPLES
18 SURVEY OF PREDICTION PRINCIPLES USING ZFC AND MORE 461
18.1 THE CLOSED UNBOUNDED FILTER 461
18.2 THE DIAMOND PRINCIPLE 462
18.3 THE WEAK DIAMOND PRINCIPLE 464
18.4 SURPRISINGLY SHORT 465
18.5 A FIRST APPLICATION OF E 468
18.5.1 THE ALGEBRAIC PART FOR PROVING END# M = A ASSUMING THE DIAMOND
PRINCIPLE 0 E AND THE WEAK DIAMOND & E . 468 18.5.2 THE CONSTRUCTION
OF I?-MODULES M WITH END M = A ASSUMING O 471
18.5.3 THE EXISTENCE OF ^-MODULES M WITH END M = A ASSUMING 2 N 2
KI 475
19 PREDICTION PRINCIPLES IN ZFC: THE BLACK BOXES AND OTHERS 478
19.1 THE EASY BLACK BOX 478
19.2 THE STRONG BLACK BOX 480
19.3 THE STRONG BLACK BOX FOR ENDOMORPHISM RINGS 480
19.4 THE STRONG BLACK BOX FOR ULTRA-COTORSION-FREE MODULES 491
19.5 THE GENERAL BLACK BOX 500
19.6 THE GENERAL BOX FOR ISF/^-ALGEBRAS 509
19.7 THE SHELAH ELEVATOR 513
19.7.1 THE COMBINATORIAL PART OF THE ELEVATOR 513
19.8 SHELAH S ABSOLUTELY RIGID FAMILY OF TREES 519
19.8.1 RIGID FAMILIES OF COLOURED TREES AND THE FIRST W-ERDOS CARDINAL
520
19.9 ABSOLUTELY RIGID TREES 521
19.9.1 PARTITION PRINCIPLES 521
19.9.2 THE EXISTENCE OF LARGE FAMILIES OF ABSOLUTELY RIGID TREES . . .
524
HTTP://D-NB.INFO/1017753385
IMAGE 2
VI
CONTENTS
V ENDOMORPHISM ALGEBRAS AND AUTOMORPHISM GROUPS
20 REALISING ALGEBRAS 531
20.1 REALISING ALGEBRAS OF SIZE 2 N 531
20.2 REALISING ALL COTORSION-FREE ALGEBRAS 542
20.2.1 THE MAIN REALISATION THEOREM AND THE STRONG BLACK BOX . . 544
20.2.2 THE MAIN REALISATION THEOREM AND THE GENERAL BLACK BOX . . 552
20.2.3 COTORSION-FREE MODULES 564
20.2.4 ALMOST COTORSION-FREE, SEPARABLE, SLENDER AND HI-FREE MODULES 566
20.2.5 ENDOMORPHISM RINGS OF BUTLER GROUPS 573
20.2.6 REALISATION THEOREMS FOR TORSION AND MIXED MODULES . . . . 573
20.3 ALGEBRAS OF ROW-AND-COLUMN-FINITE MATRICES 575
21 AUTOMORPHISM GROUPS OF TORSION-FREE ABELIAN GROUPS 578
21.1 THE HIRSCH-ZASSENHAUS-THEOREM 580
21.1.1 THE SIX PRIMORDIAL GROUPS 582
21.1.2 A CRUCIAL LEMMA AND ITS CONSEQUENCES 588
21.2 AN EXTENSION TO THE TORSION CASE 591
21.3 INVOLUTIONS OF THE GROUP OF UNITS 593
21.4 OPEN PROBLEMS 596
22 MODULES WITH DISTINGUISHED SUBMODULES 597
22.1 THE FIVE-SUBMODULE THEOREM, AN EASY APPLICATION OF THE ELEVATOR . .
597 22.2 THE FOUR-SUBMODULE THEOREM, A HARDER CASE 603
22.3 ABSOLUTELY RIGID ABELIAN GROUPS AND -RINGS OF SIZE K { LO ) DO
NOT EXIST 616
22.3.1 COUNTABLE GROUPS WITH LARGE ENDOMORPHISM RINGS 616 22.4
ABSOLUTELY INDECOMPOSABLE/?4-MODULES 619
22.4.1 THE MAIN CONSTRUCTION 619
22.4.2 EXTENSION TO FULLY RIGID SYSTEMS 622
22.4.3 PASSING TO ABSOLUTELY FULLY RIGID SYSTEMS OF /?5-MODULES . . 623
22.5 A DISCUSSION OF REPRESENTATIONS OF POSETS 625
22.5.1 SIMSON S MINIMAL POSETS V , . . . , P N O OF INFINITE
PRINJECTIVE TYPE 627
22.6 OPEN PROBLEMS 634
23 /F-MODULES AND FIELDS FROM MODULES WITH DISTINGUISHED SUBMODULES 636
23.1 MODULES: THE UNRESTRICTED CASE AND THE ABSOLUTE CASE 636
23.2 A TOPOLOGICAL REALISATION FROM THEOREM 22.21 641
23.3 APPENDIX 645
IMAGE 3
CONTENTS V I I
23.4 PRESCRIBING ENDOMORPHISM MONOIDS AND AUTOMORPHISM GROUPS OF
FIELDS 646
23.5 ABSOLUTELY RIGID FIELDS 648
23.5.1 THE TOOLS FROM FIELD THEORY FOR APPLICATIONS OF /^--MODULES . 650
23.5.2 THE CONSTRUCTION OF ABSOLUTELY ENDO-RIGID FIELDS WITH PRESCRIBED
ENDOMORPHISM MONOID 651
23.5.3 SKETCH OF THE PROOF OF THEOREM 23.25 656
23.6 OPEN PROBLEMS 658
24 ENDOMORPHISM ALGEBRAS OF K -FREE MODULES 659
24.1 N I-FREE MODULES OF CARDINALITY KI 659
24.1.1 THE CONSTRUCTION OF MODULES 660
24.1.2 THE PIGEON-HOLE LEMMA 665
24.1.3 COMPARING BRANCHING POINTS 668
24.1.4 PROOF OF THE THEOREM 672
24.2 THE NEXT STEP: H -FREE MODULES FOR ANY NATURAL NUMBER RC 6 N . . .
673 24.3 THE BASICS FOR THE NEW COMBINATORIAL BLACK BOX 675
24.3.1 THE BASICS FOR THE EASY BLACK BOX 675
24.3.2 ALGEBRAIC PRELIMINARIES FOR K -FREE MODULES 676
24.4 K -FREE ,4-MODULES 677
24.5 THE TRIPLE-HOMOMORPHISM P AND FREENESS 682
24.6 CHAINS OF TRIPLES 693
24.7 THE STEP LEMMA 695
24.7.1 THE CASE OF / = 0 698
24.7.2 THE CASE OF / 0 699
24.7.3 PREPARING THE PREDICTIONS ON G FOR THE STEP LEMMA . . . . 699
24.8 APPLICATION OF THE STRONG BLACK BOX 709
24.9 FULLY RIGID SYSTEMS OF K^-FREE R-MODULES WITH A PRESCRIBED
/^-ALGEBRA 715
24.10 OPEN PROBLEMS 716
VI MODULES AND RINGS RELATED TO ALGEBRAIC TOPOLOGY
25 LOCALISATIONS AND CELLULAR COVERS, THE GENERAL THEORY FOR /F-MODULES
719 25.1 A SKETCH OF THE CATEGORICAL SETTINGS 719
25.1.1 LOCALISATIONS REPRESENTED BY MORPHISMS 721
25.2 LOCALISATIONS NOT REPRESENTED BY MORPHISMS 723
25.3 CONSTRUCTING LOCALISATIONS OF -MODULES 726
25.4 CELLULAR COVERS OF R-MODULES 733
25.5 SOME ADDITIONS AND COSMETICS ON CELLULAR COVERS AND LOCALISATIONS .
741
IMAGE 4
V I I I
CONTENTS
25.6 EXCURSION ON LOCALISATIONS AND CELLULAR COVERS OF NON-COMMUTATIVE
GROUPS 743
25.6.1 PASSING TO LOCALISATIONS OF GROUPS 743
25.6.2 PASSING TO CELLULAR COVERS OF GROUPS 745
25.7 OPEN PROBLEMS 751
26 TAME AND WILD LOCALISATIONS OF SIZE 2^ 752
26.1 TAME LOCALISATIONS 752
26.2 THE WILD CASE: CLASSICAL (/?)-ALGEBRAS 754
26.2.1 THE DEFINITION AND ITS CONNECTION TO PROBLEMS IN ALGEBRAIC
TOPOLOGY 754
26.3 CHARACTERIZATIONS OF E(R) -ALGEBRAS 759
26.4 CONSTRUCTION OF COTORSION-FREE E(R) -ALGEBRAS OF RANK 2^ . . . .
761 26.5 (/?)-ALGEBRAS AND UNIQUELY TRANSITIVE MODULES 764
26.5.1 UT-MODULES OVER PRINCIPAL IDEAL DOMAINS 766
26.5.2 PURE-INVERTIBLE ALGEBRAS 767
26.5.3 THE INDUCTIVE STEP FOR THE CONSTRUCTION OF UT-MODULES . . . 768
26.5.4 THE CONSTRUCTION OF UT-MODULES 771
27 TAME CELLULAR COVERS 773
27.1 TAME CELLULAR COVERS OF ABELIAN GROUPS 773
27.1.1 DECOMPOSITIONS OF CELLULAR COVERS 773
27.2 CELLULAR COVERS OF DIVISIBLE GROUPS 775
27.3 CELLULAR COVERS OF TORSION AND MIXED GROUPS 778
27.4 WHEN THE ONLY CELLULAR COVERS ARE THE TRIVIAL ONES 780
27.5 OPEN PROBLEMS 781
28 WILD CELLULAR COVERS 782
28.1 CELLULAR COVERS OF SUBGROUPS OF Q 782
28.2 THE KERNELS OF RANK 2 N FOR CELLULAR COVERING MAPS 783
28.3 CHARACTERIZING KERNELS OF CELLULAR COVERS OF ABELIAN GROUPS 787
29 ABSOLUTE -RINGS 792
29.1 A VERY SIMPLE EXAMPLE SHOWS THE IDEA OF THE PROOF 793
29.2 CONSTRUCTING STRONGLY RIGID COLOURED TREES 795
29.2.1 A SHIFT MAP FOR TREES 796
29.2.2 STRONGLY RIGID TREES 799
29.3 THE CONSTRUCTION OF -RINGS 801
29.4 INVARIANT PRINCIPAL IDEALS OF R 802
29.4.1 THE MAIN THEOREM AND CONSEQUENCES 808
29.4.2 LARGE FAMILIES OF ABSOLUTE -RINGS 809
29.5 THE EXISTENCE OF ABSOLUTE -MODULES 810
29.6 OPEN PROBLEMS 812
IMAGE 5
CONTENTS
IX
VII LARGE CELLULAR COVERS, LOCALISATIONS AND E(R) -ALGEBRAS
30 LARGE KERNELS OF CELLULAR COVERS AND LARGE LOCALISATIONS 815
30.1 LARGE KERNELS OF CELLULAR COVERS 815
30.2 LARGE COTORSION-FREE (.R)-ALGEBRAS 819
30.3 LOCALISATIONS OF COTORSION-FREE MODULES 823
30.3.1 LOCALISATIONS OF FREE/^-MODULES 823
30.3.2 LOCALISATIONS OF SUBGROUPS OF Q 826
30.3.3 A REPORT ON LOCALISATIONS OF FINITE SIMPLE GROUPS 830
30.3.4 DISCUSSING KI-FREE (/?)-ALGEBRAS OF CARDINALITY HI . . . . 830
30.4 OPEN PROBLEMS 831
31 MIXED (/?)-MODULES OVER DEDEKIND DOMAINS 832
31.1 THE CONSTRUCTION OF MIXED E(R) -MODULES 836
31.1.1 (/?)-MODULES WHOSE TORSION PART IS A DIRECT SUMMAND . . . 836
31.1.2 E(R) -MODULES WHOSE TORSION PART IS NOT A DIRECT SUMMAND . 837
32 E(/?)-MODULES WITH COTORSION 840
32.1 THE CONSTRUCTION OF E(R) -ALGEBRAS WITH COTORSION 847
32.2 OPEN PROBLEMS 849
VIII SOME USEFUL CLASSES OF ALGEBRAS
33 GENERALISED (/?)-ALGEBRAS 853
33.1 BACKGROUND, STRATEGY, THE BASIC SETTING AND THE MAIN RESULT 853
33.2 THE THEORY OF SKELETONS 856
33.3 BODIES 861
33.4 TYPES 865
33.5 SMALL CANCELLATION OF TYPES 867
33.6 ARBITRARILY LARGE FREE SKELETONS 877
33.7 THE ALGEBRAIC STRUCTURE OF FREE BODIES *8Y 890
33.8 THE STEP LEMMA 892
33.9 THE MAIN CONSTRUCTION USING THE DIAMOND PRINCIPLE 904
33.10 PROOF OF THE MAIN THEOREM WITH K 905
33.11 THE MAIN CONSTRUCTION IN ZFC 906
33.12 PROOF OF THE MAIN THEOREM WITH THE GENERAL BLACK BOX 910 33.13
APPENDIX: RIGID SYSTEMS OF GENERALISED (/?)-ALGEBRAS 911 33.14 OPEN
PROBLEMS 912
IMAGE 6
X CONTENTS
34 SOME MORE USEFUL CLASSES OF ALGEBRAS 913
34.1 LEAVITT TYPE RINGS: THE DISCRETE CASE 913
34.2 ALGEBRAS WITH A HAUSDORFF TOPOLOGY 920
34.3 REALISING PARTICULAR ALGEBRAS AS ENDOMORPHISM ALGEBRAS 926
BIBLIOGRAPHY 933
INDEX 965
VOLUME 1
INTRODUCTION XVII
LIST OF SYMBOLS XXV
I SOME USEFUL CLASSES OF MODULES
1 §-COMPLETIONS 3
1.1 SUPPORT OF ELEMENTS IN B - A FIRST STEP 10
1.1.1 NORMS 11
1.2 UNCOUNTABLE S IN COMPLETIONS 12
1.3 MODULES OF CARDINALITY 2^ 14
1.3.1 ALGEBRAICALLY INDEPENDENT ELEMENTS 14
2 PURE-INJECTIVE MODULES 22
2.1 DIRECT LIMITS, FINITELY PRESENTED MODULES AND PURE SUBMODULES . . .
22 2.2 CHARACTERIZATIONS OF PURE-INJECTIVE MODULES 37
3 MITTAG-LEFFLER MODULES 47
3.1 CHARACTERIZATIONS OF MITTAG-LEFFLER MODULES 47
3.2 FLAT MITTAG-LEFFLER MODULES 60
3.3 UNIONS OF COUNTABLE PURE CHAINS OF PURE-PROJECTIVE MODULES . . . .
62 3.4 LOCALLY PROJECTIVE MODULES 65
3.5 OPEN PROBLEMS 79
4 SLENDER MODULES 80
4.1 FACTORS OF PRODUCTS AND SLENDER MODULES 80
4.1.1 RADICALS COMMUTING WITH PRODUCTS 87
4.1.2 MODULES WITH A LINEAR TOPOLOGY 91
4.1.3 CHARACTERIZING SLENDER MODULES BY EXCLUDING SUBMODULES . 100 4.2
SLENDER MODULES OVER DEDEKIND DOMAINS 104
4.3 OPEN PROBLEMS I L L
IMAGE 7
CONTENTS
XI
II APPROXIMATIONS AND COTORSION PAIRS
5 APPROXIMATIONS OF MODULES 115
5.1 PREENVELOPES AND PRECOVERS 115
5.2 COTORSION PAIRS AND TOR-PAIRS 120
5.3 MINIMAL APPROXIMATIONS 126
5.4 OPEN PROBLEMS 130
6 COMPLETE COTORSION PAIRS 131
6.1 EXT AND DIRECT LIMITS 131
6.2 THE ABUNDANCE OF COMPLETE COTORSION PAIRS 135
6.3 EXT AND INVERSE LIMITS 143
6.4 OPEN PROBLEMS 154
7 HILL LEMMA AND ITS APPLICATIONS 155
7.1 THE GENERAL VERSION OF THE HILL LEMMA 156
7.2 KAPLANSKY THEOREM FOR COTORSION PAIRS 161
7.3 C-SOCLE SEQUENCES AND FILT(C)-PRECOVERS 164
7.4 SINGULAR COMPACTNESS FOR C-FILTERED MODULES 170
7.5 ASCENDING AND DESCENDING PROPERTIES OF MODULES 174
7.6 THE RANK VERSION OF THE HILL LEMMA 180
7.7 MATLIS COTORSION AND STRONGLY FLAT MODULES 181
7.7.1 STRONGLY FLAT MODULES OVER VALUATION DOMAINS 189
7.8 OPEN PROBLEMS 195
8 DECONSTRUCTION OF THE ROOTS OF EXT 196
8.1 APPROXIMATIONS BY MODULES OF FINITE HOMOLOGICAL DIMENSIONS . . . 196
8.2 CLOSURE PROPERTIES PROVIDING FOR DECONSTRUCTION 205
8.2.1 THE TILTING CASE 205
8.2.2 THE COTILTING CASE 210
8.3 THE CLOSURE OF A COTORSION PAIR 215
9 MODULES OF PROJECTIVE DIMENSION ONE 221
9.1 STRUCTURE OF V AND W I FOR SEMIPRIME GOLDIE RINGS 221
9.2 THE CLASS LIM V 224
9.3 OPEN PROBLEMS 227
10 KAPLANSKY CLASSES AND ABSTRACT ELEMENTARY CLASSES 228
10.1 KAPLANSKY CLASSES AND DECONSTRUCTIBILITY 228
10.2 FLAT MITTAG-LEFFLER MODULES REVISITED 230
10.3 ABSTRACT ELEMENTARY CLASSES OF THE ROOTS OF EXT 240
10.4 OPEN PROBLEMS 251
IMAGE 8
X I I CONTENTS
11 INDEPENDENCE RESULTS FOR COTORSION PAIRS 253
11.1 COMPLETENESS OF COTORSION PAIRS UNDER THE DIAMOND PRINCIPLE . . . .
253 11.2 UNIFORMISATION AND COTORSION PAIRS NOT GENERATED BY A SET 258
11.3 OPEN PROBLEMS 265
12 THE LATTICE OF COTORSION PAIRS 266
12.1 ULTRA-COTORSION-FREE MODULES AND THE STRONG BLACK BOX . . 266 12.2
RATIONAL COTORSION PAIRS 275
12.3 EMBEDDING POSETS INTO THE LATTICE OF COTORSION PAIRS 283
III TILTING AND COTILTING APPROXIMATIONS
13 TILTING APPROXIMATIONS 295
13.1 TILTING MODULES 295
13.2 CLASSES OF FINITE TYPE 309
13.2.1 DECONSTRUCTION TO COUNTABLE TYPE 310
13.2.2 DEFINABILITY AND THE MITTAG-LEFFLER CONDITION 315
13.2.3 FINITE TYPE AND RESOLVING SUBCATEGORIES 320
13.3 LOCALISATION OF TILTING MODULES 324
13.4 PRODUCT-COMPLETENESS OF TILTING MODULES 325
13.5 OPEN PROBLEMS 329
14 1-TILTING MODULES AND THEIR APPLICATIONS 330
14.1 TILTING TORSION CLASSES 330
14.2 THE STRUCTURE OF 1-TILTING MODULES AND CLASSES OVER PARTICULAR
RINGS . 333 14.2.1 1-TILTING CLASSES OVER ARTIN ALGEBRAS 333
14.2.2 TILTING MODULES AND CLASSES OVER PRIIFER DOMAINS 336 14.2.3 THE
CASE OF VALUATION AND DEDEKIND DOMAINS 345
14.3 BAER MODULES 347
14.3.1 SOLUTION TO THE KAPLANSKY PROBLEM 350
14.3.2 BAER MODULES OVER HEREDITARY ARTIN ALGEBRAS 351
14.4 MATLIS LOCALISATIONS 353
14.5 OPEN PROBLEMS 363
15 COTILTING CLASSES 364
15.1 COTILTING CLASSES AND THE CLASSES OF COFINITE TYPE 364
15.2 1-COTILTING MODULES AND COTILTING TORSION-FREE CLASSES 372
15.3 COTILTING OVER PRIIFER DOMAINS 376
15.4 EXT-RIGID SYSTEMS 378
15.5 OPEN PROBLEMS 381
IMAGE 9
CONTENTS X I I I
16 TILTING AND COTILTING CLASSES OVER COMMUTATIVE NOETHERIAN RINGS 382
16.1 COTILTING CLASSES AND CHARACTERISTIC SEQUENCES 382
16.1.1 THE ONE-DIMENSIONAL CASE 382
16.1.2 THE N-DIMENSIONAL CASE 386
16.2 TILTING CLASSES OVER COMMUTATIVE NOETHERIAN RINGS 392
16.3 TILTING AND COTILTING MODULES OVER 1-GORENSTEIN RINGS 395
16.4 TOR-PAIRS OVER HEREDITARY RINGS 396
16.5 OPEN PROBLEMS 398
17 TILTING APPROXIMATIONS AND THE FINITISTIC DIMENSION CONJECTURES 400
17.1 FINITISTIC DIMENSION CONJECTURES AND THE TILTING MODULE TF 400 17.2
A FORMULA FOR THE LITTLE FINITISTIC DIMENSION OF RIGHT ARTINIAN RINGS .
. 407 17.3 ARTINIAN RINGS WITH V U CONTRAVARIANTLY FINITE 411
17.4 OPEN PROBLEMS 417
BIBLIOGRAPHY , 419
INDEX 451
|
| any_adam_object | 1 |
| author | Göbel, Rüdiger 1940-2014 Trlifaj, Jan |
| author_GND | (DE-588)1026155436 (DE-588)112022995 |
| author_facet | Göbel, Rüdiger 1940-2014 Trlifaj, Jan |
| author_role | aut aut |
| author_sort | Göbel, Rüdiger 1940-2014 |
| author_variant | r g rg j t jt |
| building | Verbundindex |
| bvnumber | BV040517866 |
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| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025364231 |
| oclc_num | 816306220 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-20 DE-19 DE-BY-UBM |
| physical | XXIV S., S. 462 - 972 graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Göbel, Rüdiger 1940-2014 Verfasser (DE-588)1026155436 aut Approximations and endomorphism algebras of modules 2 Predictions Rüdiger Göbel ; Jan Trlifaj 2., rev. and extended ed. Berlin [u.a.] de Gruyter 2012 XXIV S., S. 462 - 972 graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 41,2 De Gruyter expositions in mathematics 41 Trlifaj, Jan Verfasser (DE-588)112022995 aut (DE-604)BV040517858 2 De Gruyter expositions in mathematics 41,2 (DE-604)BV004069300 41,2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025364231&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Göbel, Rüdiger 1940-2014 Trlifaj, Jan Approximations and endomorphism algebras of modules De Gruyter expositions in mathematics |
| title | Approximations and endomorphism algebras of modules |
| title_auth | Approximations and endomorphism algebras of modules |
| title_exact_search | Approximations and endomorphism algebras of modules |
| title_full | Approximations and endomorphism algebras of modules 2 Predictions Rüdiger Göbel ; Jan Trlifaj |
| title_fullStr | Approximations and endomorphism algebras of modules 2 Predictions Rüdiger Göbel ; Jan Trlifaj |
| title_full_unstemmed | Approximations and endomorphism algebras of modules 2 Predictions Rüdiger Göbel ; Jan Trlifaj |
| title_short | Approximations and endomorphism algebras of modules |
| title_sort | approximations and endomorphism algebras of modules predictions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025364231&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040517858 (DE-604)BV004069300 |
| work_keys_str_mv | AT gobelrudiger approximationsandendomorphismalgebrasofmodules2 AT trlifajjan approximationsandendomorphismalgebrasofmodules2 |