A radical approach to algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1970
|
| Series: | Addison-Wesley series in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 232 S. |
Staff View
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Record in the Search Index
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| adam_text | Contents
Chapter 1 Rings and Ideals
Section 1 Definition and examples 1
Section 2 Ideals , 4
Section 3 Quotient rings and homomorphisms 8
Section 4 The field of quotients 10
Section 5 Minimal and maximal conditions 11
Section 6 Primary decomposition 13
Section 7 Unique factorization domains 17
Section 8 Polynomial rings 20
Chapter 2 The Classical Radical
Section 1 Nilpotent ideals and the radical 27
Section 2 The radical of related rings 29
Section 3 Artinian rings 30
Section 4 Direct sum decompositions 32
Section 5 Ideals in semisimple rings 34
Section 6 Matrix rings 36
Section 7 The Wedderburn theorem 40
Chapter 3 Modules
Section 1 Preliminaries 43
Section 2 Direct sums and free modules 46
Section 3 Projective modules 53
Section 4 Horn 55
Section 5 Tensor products 61
Section 6 Algebras 66
Chapter 4 The Jacobson Radical
Section 1 Definition of the Jacobson radical 73
Section 2 Properties 75
Section 3 Jacobson radicals of related rings 79
Section 4 Primitive rings 84
Section 5 The density theorem 85
Section 6 Structure theorems 88
vi
Contents vii
Chapter 5 Other Radicals and Radical Properties
Section 1 Radical ideals 91
Section 2 The Levitzki radical 94
Section 3 Brown McCoy radicals .96
Section 4 Amitsur s properties 104
Section 5 Results of Nagata 105
Section 6 Relations among the radicals 107
Section 7 More about radical properties 109
Chapter 6 Generalizations to Other Systems
Section 1 Algebras 114
Section 2 Group algebras 117
Section 3 Near rings 120
Section 4 Groups 122
Section 5 Radicals in lattices 125
Section 6 Abstract algebras 130
Chapter 7 Lie and Jordan Algebras
Section 1 Definitions and examples 133
Section 2 Albert s radical 136
Section 3 Nilpotency and solvability 137
Section 4 A structure theorem for nonassociative algebras 138
Section 5 Jordan algebras 139
Section 6 Lie algebras 141
Section 7 Simple Lie and Jordan algebras 149
Chapter 8 Category Theory
Section 1 Definition and examples 152
Section 2 Functors 154
Section 3 Objects and morphisms 156
Section 4 Kernels and images 159
Section 5 Exact categories 163
Section 6 Products and limits 167
Section 7 Abelian categories 171
Section 8 More about functors 177
Chapter 9 Radical Subcategories
Section 1 Semi abelianess 182
Section 2 Radical and coradical subcategories 185
Section 3 Properties of radicals and coradicals 187
Section 4 Abelian objects 189
Section 5 Categorical characterization of group algebras 197
viii Contents
Chapter 10 Applications of Sheaf Theory to the Study of Rings
Section 1 The structure space of a ring 202
Section 2 Biregular rings 205
Section 3 Sheaves 209
Section 4 Representation of biregular rings 211
Section 5 Boolean ring modules 217
Selected Bibliography 221
Index 227
|
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| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:48:56Z |
| institution | BVB |
| language | English |
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| physical | VIII, 232 S. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley series in mathematics |
| spelling | Gray, Mary Verfasser (DE-588)116827831 aut A radical approach to algebra Mary Gray Reading, Mass. [u.a.] Addison-Wesley 1970 VIII, 232 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Algebra Associativa larpcal Algèbre Algebra Radikal Mathematik (DE-588)4176796-2 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 Radikal Mathematik (DE-588)4176796-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001753028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gray, Mary A radical approach to algebra Algebra Associativa larpcal Algèbre Algebra Radikal Mathematik (DE-588)4176796-2 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4176796-2 (DE-588)4001156-2 |
| title | A radical approach to algebra |
| title_auth | A radical approach to algebra |
| title_exact_search | A radical approach to algebra |
| title_full | A radical approach to algebra Mary Gray |
| title_fullStr | A radical approach to algebra Mary Gray |
| title_full_unstemmed | A radical approach to algebra Mary Gray |
| title_short | A radical approach to algebra |
| title_sort | a radical approach to algebra |
| topic | Algebra Associativa larpcal Algèbre Algebra Radikal Mathematik (DE-588)4176796-2 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra Associativa Algèbre Algebra Radikal Mathematik |
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