Lifting modules: supplements and projectivy in module theory
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2006
|
| Series: | Frontiers in mathematics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 363 - 385 |
| Physical Description: | XII, 394 S. 24 cm |
| ISBN: | 9783764375720 3764375728 |
Staff View
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| 245 | 1 | 0 | |a Lifting modules |b supplements and projectivy in module theory |c John Clark ... |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2006 | |
| 300 | |a XII, 394 S. |c 24 cm | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
vii
Introduction
ix
Notation
xiii
1
Basic notions
1
1
Preliminaries
.............................. 1
2
Small
submodules
and the
radical
................... 11
3
Cosmall inclusions and coclosed submodules
............. 20
4
Projectivity conditions
......................... 26
5
Hollow
dimension
of
modules
..................... 47
2
Preradicals and torsion
theories
55
6
Preradicals and colocalisation
..................... 55
7
Torsion
theories
............................. 70
8
Torsion
theories related to small modules
.............. 74
9
Corational modules
........................... 84
10
Proper classes and
т
-supplements...................
94
3
Decompositions of modules
103
11
The exchange property
......................... 103
12
LE-modules and local semi-T-nilpotency
............... 124
13
Local direct summands
......................... 142
14
The total and LE-decompositions
................... 162
15
Stable range
1
and cancellation
.................... 180
16
Decomposition uniqueness and biuniformity
............. 194
4
Supplements in modules
207
17
Semilocal and weakly supplemented modules
............ 207
18
Weak supplements and hollow dimension
............... 218
19
Semilocal endomorphism rings
.................... 227
20
Supplemented modules
......................... 233
21
Submodules
with unique coclosure
.................. 257
vi
Contents
5
From lifting to perfect modules
265
22
Lifting modules
............................. 265
23
Finite direct sums of lifting modules
................. 277
24
The lifting property for infinite sums
................. 289
25
Σ
-lifting
modules
............................ 296
26
Semi-discrete and quasi-discrete modules
............... 307
27
Discrete and perfect modules
..................... 317
28
Injective modules lifting in
σ[Μ]
................... 331
29
Extending modules lifting in
σ[Μ]
.................. 347
Appendix
359
30
Hall s Marriage Theorem
........................ 359
31 König s
Graph Theorem
........................ 362
Bibliography
363
Index
387
|
| adam_txt |
Contents
Preface
vii
Introduction
ix
Notation
xiii
1
Basic notions
1
1
Preliminaries
. 1
2
Small
submodules
and the
radical
. 11
3
Cosmall inclusions and coclosed submodules
. 20
4
Projectivity conditions
. 26
5
Hollow
dimension
of
modules
. 47
2
Preradicals and torsion
theories
55
6
Preradicals and colocalisation
. 55
7
Torsion
theories
. 70
8
Torsion
theories related to small modules
. 74
9
Corational modules
. 84
10
Proper classes and
т
-supplements.
94
3
Decompositions of modules
103
11
The exchange property
. 103
12
LE-modules and local semi-T-nilpotency
. 124
13
Local direct summands
. 142
14
The total and LE-decompositions
. 162
15
Stable range
1
and cancellation
. 180
16
Decomposition uniqueness and biuniformity
. 194
4
Supplements in modules
207
17
Semilocal and weakly supplemented modules
. 207
18
Weak supplements and hollow dimension
. 218
19
Semilocal endomorphism rings
. 227
20
Supplemented modules
. 233
21
Submodules
with unique coclosure
. 257
vi
Contents
5
From lifting to perfect modules
265
22
Lifting modules
. 265
23
Finite direct sums of lifting modules
. 277
24
The lifting property for infinite sums
. 289
25
Σ
-lifting
modules
. 296
26
Semi-discrete and quasi-discrete modules
. 307
27
Discrete and perfect modules
. 317
28
Injective modules lifting in
σ[Μ]
. 331
29
Extending modules lifting in
σ[Μ]
. 347
Appendix
359
30
Hall's Marriage Theorem
. 359
31 König's
Graph Theorem
. 362
Bibliography
363
Index
387 |
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| discipline | Mathematik |
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| isbn | 9783764375720 3764375728 |
| language | English |
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| physical | XII, 394 S. 24 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Frontiers in mathematics |
| spelling | Lifting modules supplements and projectivy in module theory John Clark ... Basel [u.a.] Birkhäuser 2006 XII, 394 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Frontiers in mathematics Literaturverz. S. 363 - 385 Modultheorie (DE-588)4170336-4 gnd rswk-swf Liften Mathematik (DE-588)4167655-5 gnd rswk-swf Modultheorie (DE-588)4170336-4 s Liften Mathematik (DE-588)4167655-5 s DE-604 Clark, John Sonstige oth text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2754533&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015043584&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lifting modules supplements and projectivy in module theory Modultheorie (DE-588)4170336-4 gnd Liften Mathematik (DE-588)4167655-5 gnd |
| subject_GND | (DE-588)4170336-4 (DE-588)4167655-5 |
| title | Lifting modules supplements and projectivy in module theory |
| title_auth | Lifting modules supplements and projectivy in module theory |
| title_exact_search | Lifting modules supplements and projectivy in module theory |
| title_exact_search_txtP | Lifting modules supplements and projectivy in module theory |
| title_full | Lifting modules supplements and projectivy in module theory John Clark ... |
| title_fullStr | Lifting modules supplements and projectivy in module theory John Clark ... |
| title_full_unstemmed | Lifting modules supplements and projectivy in module theory John Clark ... |
| title_short | Lifting modules |
| title_sort | lifting modules supplements and projectivy in module theory |
| title_sub | supplements and projectivy in module theory |
| topic | Modultheorie (DE-588)4170336-4 gnd Liften Mathematik (DE-588)4167655-5 gnd |
| topic_facet | Modultheorie Liften Mathematik |
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