Cogroups and co-rings in categories of associative rings:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1996]
|
| Series: | Mathematical surveys and monographs
Volume 45 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | ix, 388 Seiten Diagramme |
| ISBN: | 0821804952 9780821804957 |
Staff View
MARC
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| 245 | 1 | 0 | |a Cogroups and co-rings in categories of associative rings |c George M. Bergman ; Adam O. Hausknecht |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Chapter I. Introduction
0. General prerequisites 1
1. Introductory sketch what are coalgebras, and why? 1
2. Overview of results 4
3. Results in the literature 6
4. Notes on this book; acknowledgements 7
Chapter II. Review of coalgebras and representable functors
5. Category theoretic formulations of universal properties, and some
other matters 9
6. Basic definitions and results of universal algebra 18
7. Some conventions followed throughout this work 19
8. Algebra and coalgebra objects in a category, and representable
algebra valued functors 20
9. Digressions on representable functors 30
Chapter III. Representable functors from rings to abelian groups
10. it Rings 35
11. Representable functors and pointed categories 39
12. Plans and preparations 41
13. Proof of the structure theorem for co AbSemigp e objects 47
14. Some immediate consequences 55
Chapter IV. Digressions on semigroups, etc.
15. Representable functors to AbBinare 61
16. Representable functors to abelian semigroups without neutral
element easy results 63
17. Symmetry conditions, and cocommutativity 68
18. Application to AbSemigp valued functors 74
19. Some observations and questions on rings of symmetric elements 78
20. Representable functors from Semigpe to Semigpe 82
21. Representable functors among varieties of groups and semigroups 89
22. Some related varieties: binars, heaps, and Mal cev algebras 95
vii
viii CONTENTS
Chapter V. Representable functors from algebras over a field to rings
23. Bilinear maps 99
24. Review of linearly compact vector spaces 104
25. Functors to associative rings, Lie rings, and Jordan rings 114
26. Functors to other subvarieties of NARing 128
27. A Galois connection 136
Chapter VI. Representable functors from rings to rings
28. Element chasing without elements 146
29. ®k co rings 149
30. Subfunctors of forgetful functors, and a result of Sweedler 154
31. Images of morphisms 161
32. A non locally finite ®^ coalgebra 172
Chapter VII. Representable functors from rings to general groups and
semigroups
33. Functors to Group 175
34. Functors on connected graded rings 179
35. Functors from ^ algebras to semigroups: some examples 190
36. Jacobson radicals, and a general construction 194
37. Representable functors to semigroups: toward some conjectures 200
38. Density of invertible elements 202
39. An idempotentless example, and a question on subfunctors.... 206
Chapter VIII. Representable functors on categories of commutative
associative algebras
40. Some easy examples 210
41. Identities and equational subfunctors 214
42. Idempotents again 224
43. Bialgebras and Hopf algebras 230
44. The Witt vector construction 237
45. The co ring of integral polynomials 240
46. Generalized integral polynomials 243
47. Representative functions and linearly recursive sequences 246
48. A last tantalizing observation on idempotents 256
Chapter IX. Representable functors on categories of Lie algebras
49. Generalities and conventions 259
50. Abelian group valued and ring valued functors: positive results 261
51. Counterexamples in characteristic p 269
52. Functors Lie^ — Group 274
CONTENTS ix
Chapter X. Multilinear algebra of representable functors on R«ng
53. Multilinear maps, and tensor products of representable functors 277
54. Higher degree maps of Ab valued functors 280
55. Higher degree maps between modules 285
56. Functors to generalized Jordan rings 291
Chapter XL Directions for further investigation
57. Other varieties of algebras 295
58. Some miscellaneous remarks 299
59. Prevarieties 303
60. ® algebras and ® coalgebras 309
61. Further observations on ® 316
62. Analogs of ® 319
63. Tall Wraith monads and hermaphroditic functors 326
64. Examples of TW monads, and further remarks 333
65. The Ehrenfeucht question for semigroups and associative algebras 341
References 348
Word and phrase index 360
Symbol index 380
end 388
Dependence of sections
All parts of these notes assume the material of Chapter II; or more
precisely, the first four sections thereof. The statement of the main result of
Chapter III, Theorem 13.15, is also assumed in all subsequent Chapters
except VIII. (Partial exceptions: the last three sections of Chapter IV do not
require this result, though they assume familiarity with the notational
approach of §12; nor, for the most part, do §39, §§59 63 or §65.)
The Chapters after III are mutually independent, except that Chapter V is
assumed in Chapters VI and IX, and in §57 and §64; and its first section,
§23, in Chapter X as well.
Within each Chapter, later sections generally assume the earlier ones.
Notable exceptions are Chapter IV, where the last three sections are
independent of the first five, Chapter VII, where the last section is self
contained, and the final chapter, which breaks into largely self contained
sequences {57, 58}, {59, 65}, {60, 61, 62} and {63, 64}.
There are minor dependencies not noted above (for instance, some of the
definitions, though not the results, of §§28 29 are called on at various
places). Thus, the reader following a shortcut through the text based on the
above notes will occasionally have to backtrack, using an internal cross
reference or the index to locate the material required.
|
| any_adam_object | 1 |
| author | Bergman, George M. 1943- Hausknecht, Adam O. |
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| indexdate | 2024-07-09T18:00:14Z |
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| language | English |
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| physical | ix, 388 Seiten Diagramme |
| publishDate | 1996 |
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| spelling | Bergman, George M. 1943- Verfasser (DE-588)172970725 aut Cogroups and co-rings in categories of associative rings George M. Bergman ; Adam O. Hausknecht Providence, Rhode Island American Mathematical Society [1996] © 1996 ix, 388 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 45 Anneaux associatifs ram Catégories (Mathématiques) ram Foncteurs, théorie des ram Associative rings Categories (Mathematics) Corings (Algebra) Equipment Safety Fires prevention & control Functor theory Power Plants standards Assoziativer Ring (DE-588)4143228-9 gnd rswk-swf Funktorkategorie (DE-588)4155700-1 gnd rswk-swf Assoziativer Ring (DE-588)4143228-9 s Funktorkategorie (DE-588)4155700-1 s DE-604 Hausknecht, Adam O. Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4704-1276-0 Mathematical surveys and monographs Volume 45 (DE-604)BV000018014 45 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007264241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bergman, George M. 1943- Hausknecht, Adam O. Cogroups and co-rings in categories of associative rings Mathematical surveys and monographs Anneaux associatifs ram Catégories (Mathématiques) ram Foncteurs, théorie des ram Associative rings Categories (Mathematics) Corings (Algebra) Equipment Safety Fires prevention & control Functor theory Power Plants standards Assoziativer Ring (DE-588)4143228-9 gnd Funktorkategorie (DE-588)4155700-1 gnd |
| subject_GND | (DE-588)4143228-9 (DE-588)4155700-1 |
| title | Cogroups and co-rings in categories of associative rings |
| title_auth | Cogroups and co-rings in categories of associative rings |
| title_exact_search | Cogroups and co-rings in categories of associative rings |
| title_full | Cogroups and co-rings in categories of associative rings George M. Bergman ; Adam O. Hausknecht |
| title_fullStr | Cogroups and co-rings in categories of associative rings George M. Bergman ; Adam O. Hausknecht |
| title_full_unstemmed | Cogroups and co-rings in categories of associative rings George M. Bergman ; Adam O. Hausknecht |
| title_short | Cogroups and co-rings in categories of associative rings |
| title_sort | cogroups and co rings in categories of associative rings |
| topic | Anneaux associatifs ram Catégories (Mathématiques) ram Foncteurs, théorie des ram Associative rings Categories (Mathematics) Corings (Algebra) Equipment Safety Fires prevention & control Functor theory Power Plants standards Assoziativer Ring (DE-588)4143228-9 gnd Funktorkategorie (DE-588)4155700-1 gnd |
| topic_facet | Anneaux associatifs Catégories (Mathématiques) Foncteurs, théorie des Associative rings Categories (Mathematics) Corings (Algebra) Equipment Safety Fires prevention & control Functor theory Power Plants standards Assoziativer Ring Funktorkategorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007264241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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