A radical approach to algebra
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
1970
|
| Schriftenreihe: | Addison-Wesley series in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV002741775 | ||
| 003 | DE-604 | ||
| 005 | 20090710 | ||
| 007 | t| | ||
| 008 | 900620s1970 xx |||| 00||| eng d | ||
| 035 | |a (OCoLC)251610443 | ||
| 035 | |a (DE-599)BVBBV002741775 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-384 |a DE-703 |a DE-355 |a DE-824 |a DE-29T |a DE-706 |a DE-188 | ||
| 050 | 0 | |a QA251 | |
| 082 | 0 | |a 512.8 |2 18 | |
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 100 | 1 | |a Gray, Mary |e Verfasser |0 (DE-588)116827831 |4 aut | |
| 245 | 1 | 0 | |a A radical approach to algebra |c Mary Gray |
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1970 | |
| 300 | |a VIII, 232 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Addison-Wesley series in mathematics | |
| 650 | 7 | |a Algebra Associativa |2 larpcal | |
| 650 | 4 | |a Algèbre | |
| 650 | 4 | |a Algebra | |
| 650 | 0 | 7 | |a Radikal |g Mathematik |0 (DE-588)4176796-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Radikal |g Mathematik |0 (DE-588)4176796-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 2 | 1 | |a Radikal |g Mathematik |0 (DE-588)4176796-2 |D s |
| 689 | 2 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-001753028 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 110f 2001 A 16145 0102 MAT 110f 2001 A 16144 |
|---|---|
| DE-BY-TUM_katkey | 481589 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010614158 040010614169 |
| _version_ | 1820873878640001024 |
| 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
|
| any_adam_object | 1 |
| author | Gray, Mary |
| author_GND | (DE-588)116827831 |
| author_facet | Gray, Mary |
| author_role | aut |
| author_sort | Gray, Mary |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | BV002741775 |
| callnumber-first | Q - Science |
| callnumber-label | QA251 |
| callnumber-raw | QA251 |
| callnumber-search | QA251 |
| callnumber-sort | QA 3251 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)251610443 (DE-599)BVBBV002741775 |
| dewey-full | 512.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.8 |
| dewey-search | 512.8 |
| dewey-sort | 3512.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01619nam a2200445 c 4500</leader><controlfield tag="001">BV002741775</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090710 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">900620s1970 xx |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)251610443</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002741775</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA251</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.8</subfield><subfield code="2">18</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gray, Mary</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)116827831</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A radical approach to algebra</subfield><subfield code="c">Mary Gray</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Reading, Mass. [u.a.]</subfield><subfield code="b">Addison-Wesley</subfield><subfield code="c">1970</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 232 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Addison-Wesley series in mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Algebra Associativa</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algèbre</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Radikal</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4176796-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Radikal</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4176796-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Radikal</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4176796-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001753028</subfield></datafield></record></collection> |
| id | DE-604.BV002741775 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T10:47:10Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001753028 |
| oclc_num | 251610443 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-188 |
| physical | VIII, 232 S. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley series in mathematics |
| 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 |
| url | 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 |
| work_keys_str_mv | AT graymary aradicalapproachtoalgebra |