Regularity and substructures of Hom:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2009
|
| Series: | Frontiers in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 164 S. |
| ISBN: | 9783764399894 |
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MARC
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| 245 | 1 | 0 | |a Regularity and substructures of Hom |c Friedrich Kasch ; Adolf Mader |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2009 | |
| 300 | |a XV, 164 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Frontiers in mathematics | |
| 650 | 4 | |a Homomorphismus - Regularität | |
| 650 | 4 | |a Homomorphisms (Mathematics) | |
| 650 | 4 | |a Modules (Algebra) | |
| 650 | 4 | |a Rings (Algebra) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
vii
I Notation and Background
1
1
Notation
................................. 1
2
Rings and Modules
........................... 2
3
Abelian Groups
............................. 6
II Regular Homomorphisms
11
1
Definition and Characterization
.................... 11
2
Partially
Invertitile
Homomorphisms and
Quasi-Inverses
...... 15
3
Regular Homomorphisms Generate
Projective
Direct Summands
. 19
4
Existence and Properties of Reg(A, M)
................ 21
5
The Transfer Rule
........................... 25
6
Inherited Regularity
.......................... 26
7
Appendix: Various Formulas
...................... 39
III Indecomposable Modules
41
1
Reg(A,
Μ) φ
0............................. 41
2
Structure Theorems
.......................... 42
IV Regularity in Modules
49
1
Pandamental
Results
.......................... 49
2
Quasi-Inverses
.............................. 52
2.1
Basic Properties
........................ 52
2.2
Partially Invertible Objects are
Quasi-Inverses
....... 53
3
Regular Elements Generate
Projective
Direct Summands
...... 54
4
Remarks on the Literature
....................... 56
5
The Transfer Rule
........................... 57
V Regularity in
Ћошц(А,
M) as a
One-sided Module
59
1
Iterated Endomorphism Rings
..................... 59
2
Definitions and Characterizations
................... 60
vi
Contents
3
Largest Regular
Submodules
..................... 65
4
The Transfer Rule for S-Regularity
.................. 66
VI Relative Regularity: U-Regularity and Semiregularity
69
1
řJ-Regularity;
Definition and Existence of
ř/-Reg(A,
M)......
69
2
[/-Regularity in Modules
........................ 72
3
Semiregularity for Modules
...................... 73
4
Semiregularity for
Hom
........................ 76
VII
Reg(A
M)
and Other Substructures of
Hom
81
1
Substructures of
Hom
......................... 81
2
Properties of
Δ(Α, Μ)
and V(A, M)
................. 85
3
The Special Case
Нотл(Л,
M)....................
87
4
Further Internal Properties of
Δ(Μ)
................. 90
5
Non-singular Modules
......................... 94
6
A Correspondenc Between
Submodules
of
Нотд(А,
M)
and Ideals
ofEnd(MR)
............................... 95
7
Correspondences for Modules
..................... 100
VIII
Regularity in Homomorphism Groups of Abelian Groups
103
1
Introduction
............................... 103
2
Hom(A M)
and Regularity
...................... 103
3
Mixed Groups
.............................. 115
4
Regularity in Endomorphism Rings of Mixed Groups
........ 127
IX Regularity in Categories
131
1
Regularity in Preadditive Categories
................. 131
2
Preadditive Categories
......................... 132
3
The Qiiasi-Isomorphism Category of Torsion-free Abelian Groups
. 137
4
Regularity in QA
............................ 150
4.1
Realizing Q(v/p)
........................ 153
4.2
Constructing the Group
.................... 153
4.3
Computing the Quasi-Endomorphism Ring
......... 154
5
Regularity in the Category of Groups
................ 155
Bibliography
157
Index
161
|
| any_adam_object | 1 |
| author | Kasch, Friedrich 1921-2017 Mader, Adolf |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512.42 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035674261 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:43:01Z |
| institution | BVB |
| isbn | 9783764399894 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017728489 |
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| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-384 |
| physical | XV, 164 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Frontiers in mathematics |
| spelling | Kasch, Friedrich 1921-2017 Verfasser (DE-588)117713937 aut Regularity and substructures of Hom Friedrich Kasch ; Adolf Mader Basel [u.a.] Birkhäuser 2009 XV, 164 S. txt rdacontent n rdamedia nc rdacarrier Frontiers in mathematics Homomorphismus - Regularität Homomorphisms (Mathematics) Modules (Algebra) Rings (Algebra) Regularität (DE-588)4049074-9 gnd rswk-swf Homomorphismus (DE-588)4160602-4 gnd rswk-swf Homomorphismus (DE-588)4160602-4 s Regularität (DE-588)4049074-9 s DE-604 Mader, Adolf Verfasser (DE-588)117711578 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728489&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kasch, Friedrich 1921-2017 Mader, Adolf Regularity and substructures of Hom Homomorphismus - Regularität Homomorphisms (Mathematics) Modules (Algebra) Rings (Algebra) Regularität (DE-588)4049074-9 gnd Homomorphismus (DE-588)4160602-4 gnd |
| subject_GND | (DE-588)4049074-9 (DE-588)4160602-4 |
| title | Regularity and substructures of Hom |
| title_auth | Regularity and substructures of Hom |
| title_exact_search | Regularity and substructures of Hom |
| title_full | Regularity and substructures of Hom Friedrich Kasch ; Adolf Mader |
| title_fullStr | Regularity and substructures of Hom Friedrich Kasch ; Adolf Mader |
| title_full_unstemmed | Regularity and substructures of Hom Friedrich Kasch ; Adolf Mader |
| title_short | Regularity and substructures of Hom |
| title_sort | regularity and substructures of hom |
| topic | Homomorphismus - Regularität Homomorphisms (Mathematics) Modules (Algebra) Rings (Algebra) Regularität (DE-588)4049074-9 gnd Homomorphismus (DE-588)4160602-4 gnd |
| topic_facet | Homomorphismus - Regularität Homomorphisms (Mathematics) Modules (Algebra) Rings (Algebra) Regularität Homomorphismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728489&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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