Some topics in algebra: an advanced undergraduate course at PKU
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2014
|
| Schriftenreihe: | Mathematical Lectures from Peking University
|
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=4431371&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026904446&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 199 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642412688 9783642412684 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1819248756549222400 |
|---|---|
| adam_text | CONTENTS
1 RINGS AND POLYNOMIAL ALGEBRAS 1
1.1 FIRST DEFINITIONS 1
1.1.1 RINGS 1
1.1.2 CANONICAL MORPHISMS 9
1.1.3 IDEALS 12
1.1.4 ALGEBRAS 15
1.1.5 FIELDS, DIVISION RINGS 20
1.2 PRIME AND MAXIMAL IDEALS, INTEGRAL DOMAINS 36
1.2.1 DEFINITION AND FIRST EXAMPLES 36
1.2.2 EXAMPLES IN POLYNOMIAL RINGS 37
1.2.3 NILRADICAL AND RADICAL 39
1.2.4 INTEGRAL DOMAINS, FIELDS OF FRACTIONS 42
1.3 DIVISIBILITY AND IRREDUCIBLE ELEMENTS 47
1.3.1 DIVISORS AND IRREDUCIBLE ELEMENTS 47
1.3.2 EUCLIDEAN RINGS 49
1.3.3 GCD AND LCM 51
1.3.4 CASE OF Z[I] AND APPLICATION 52
1.3.5 IRREDUCIBILITY CRITERIA IN/?[X] 54
1.4 POLYNOMIAL RINGS IN SEVERAL INDETERMINATES 66
1.4.1 UNIVERSAL PROPERTY, SUBSTITUTIONS 66
1.4.2 TRANSFER PROPERTIES 70
1.4.3 SYMMETRIC POLYNOMIALS 71
1.4.4 RESULTANT AND DISCRIMINANT 76
2 MODULES 87
2.1 DEFINITIONS AND CONVENTIONS 87
2.1.1 DEFINITIONS 87
2.1.2 SUBMODULES 90
2.1.3 TORSION ELEMENTS, TORSION SUBMODULE 96
2.1.4 FREE AND GENERATING SYSTEMS, FREE MODULES 98
2.1.5 CONSTRUCTIONS: DIRECT SUMS, PRODUCTS, TENSOR PRODUCTS . 102
XI
HTTP://D-NB.INFO/1038868270
XII CONTENTS
2.1.6 LOCALIZATION 110
2.2 FINITELY GENERATED MODULES 115
2.2.1 APPLICATION: INTEGRALITY OVER A RING 116
2.2.2 COMPLEMENT: JACOBSON RINGS, HILBERT S NULLSTELLENSATZ . 122
2.2.3 NOETHERIAN RINGS AND MODULES 127
2.2.4 FINITELY GENERATED FREE MODULES 132
2.2.5 FINITELY GENERATED PROJECTIVE MODULES 137
2.3 FINITELY GENERATED MODULES OVER DEDEKIND DOMAINS 146
2.3.1 FRACTIONAL MODULES, DEDEKIND DOMAINS 146
2.3.2 FINITELY GENERATED PROJECTIVE MODULES OVER DEDEKIND-
DOMAINS 154
2.3.3 REMARKABLE DECOMPOSITIONS OF FINITELY GENERATED
TORSION MODULES 159
2.3.4 ADAPTED PSEUDO-BASES FOR SUBMODULES OF FINITELY
GENERATED PROJECTIVE MODULES 169
2.3.5 APPLICATIONS TO ABELIAN GROUPS AND ENDOMORPHISMS
OF VECTOR SPACES 175
2.4 COMPLEMENT ON DEDEKIND DOMAINS 186
2.4.1 CHARACTERIZATIONS OF DEDEKIND DOMAINS 186
2.4.2 RINGS OF INTEGERS OF NUMBER FIELDS ARE DEDEKIND .... 188
REFERENCES 195
INDEX 197
|
| any_adam_object | 1 |
| author | Broué, Michel 1946- |
| author_GND | (DE-588)113828853 |
| author_facet | Broué, Michel 1946- |
| author_role | aut |
| author_sort | Broué, Michel 1946- |
| author_variant | m b mb |
| building | Verbundindex |
| bvnumber | BV041458028 |
| classification_rvk | SK 200 SK 230 |
| ctrlnum | (OCoLC)864547056 (DE-599)DNB1038868270 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-12-20T16:47:48Z |
| institution | BVB |
| isbn | 3642412688 9783642412684 |
| language | English |
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| oclc_num | 864547056 |
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| owner_facet | DE-11 DE-188 DE-83 |
| physical | XII, 199 S. Ill., graph. Darst. 235 mm x 155 mm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series2 | Mathematical Lectures from Peking University |
| spellingShingle | Broué, Michel 1946- Some topics in algebra an advanced undergraduate course at PKU Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4123623-3 |
| title | Some topics in algebra an advanced undergraduate course at PKU |
| title_auth | Some topics in algebra an advanced undergraduate course at PKU |
| title_exact_search | Some topics in algebra an advanced undergraduate course at PKU |
| title_full | Some topics in algebra an advanced undergraduate course at PKU Michel Broué |
| title_fullStr | Some topics in algebra an advanced undergraduate course at PKU Michel Broué |
| title_full_unstemmed | Some topics in algebra an advanced undergraduate course at PKU Michel Broué |
| title_short | Some topics in algebra |
| title_sort | some topics in algebra an advanced undergraduate course at pku |
| title_sub | an advanced undergraduate course at PKU |
| topic | Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra Lehrbuch |
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