Prüfer domains:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Dekker
1997
|
| Schriftenreihe: | Pure and applied mathematics
203 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007434145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Abstract: | This timely reference offers - for the first time in book form - an exhaustive examination of many important developments in the theory of Prufer domains that have occurred over the past 25 years. Providing an integrated presentation of both research advances and analysis techniques, Prufer Domains covers the solution of the problem of finding the number of generators needed for a finitely generated ideal of a Prufer domain... concrete representations of particular overrings determined by ideals of R...various recently developed trace properties...polynomial rings over Prufer domains... extensions and generalizations of the originals theory...and more. Written by three acknowledged experts in the field, Prufer Domains is an excellent resource for pure and applied mathematicians, particularly algebraists and number theorists, and upper-level undergraduate and graduate students in the disciplines. |
| Umfang: | IX, 328 S. |
| ISBN: | 0824798163 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011097255 | ||
| 003 | DE-604 | ||
| 005 | 20091203 | ||
| 007 | t| | ||
| 008 | 961204s1997 xx |||| 00||| eng d | ||
| 020 | |a 0824798163 |9 0-8247-9816-3 | ||
| 035 | |a (OCoLC)35095951 | ||
| 035 | |a (DE-599)BVBBV011097255 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-739 |a DE-12 |a DE-703 | ||
| 050 | 0 | |a QA247 | |
| 082 | 0 | |a 512/.4 |2 20 | |
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 100 | 1 | |a Fontana, Marco |d 1947- |e Verfasser |0 (DE-588)139350543 |4 aut | |
| 245 | 1 | 0 | |a Prüfer domains |c Marco Fontana ; James A. Huckaba ; Ira J. Papick |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1997 | |
| 300 | |a IX, 328 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 203 | |
| 520 | 3 | |a This timely reference offers - for the first time in book form - an exhaustive examination of many important developments in the theory of Prufer domains that have occurred over the past 25 years. Providing an integrated presentation of both research advances and analysis techniques, Prufer Domains covers the solution of the problem of finding the number of generators needed for a finitely generated ideal of a Prufer domain... concrete representations of particular overrings determined by ideals of R...various recently developed trace properties...polynomial rings over Prufer domains... extensions and generalizations of the originals theory...and more. Written by three acknowledged experts in the field, Prufer Domains is an excellent resource for pure and applied mathematicians, particularly algebraists and number theorists, and upper-level undergraduate and graduate students in the disciplines. | |
| 650 | 7 | |a Anneaux (algèbre) |2 ram | |
| 650 | 4 | |a Prüfer rings | |
| 650 | 0 | 7 | |a Prüfer-Ring |0 (DE-588)4520857-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Prüfer-Ring |0 (DE-588)4520857-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Huckaba, James A. |e Verfasser |4 aut | |
| 700 | 1 | |a Papick, Ira J. |e Verfasser |4 aut | |
| 830 | 0 | |a Pure and applied mathematics |v 203 |w (DE-604)BV000001885 |9 203 | |
| 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=007434145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007434145 | |
Datensatz im Suchindex
| _version_ | 1819280370602868736 |
|---|---|
| adam_text | Contents
Preface
Chapter I. Preliminaries 1
Notes 11
Chapter II. Generating Ideals in Priifer Domains 13
2.1. Formally real fields 13
2.2. Schiilting s example 17
2.3. Bounding the generators 26
Notes 31
Chapter III. Particular Overrings of Priifer Domains 33
3.1. When is/ 1 a ring? 34
3.2. Other representation theorems 46
3.3. When equalities occur among overrings 51
Notes 57
Chapter IV. Applications of the Theory of Overrings 61
4.1. Divisorial ideals 61
4.2. Trace properties 72
4.3. When all ideals are divisorial 100
4.4. A-extensions 104
4.5. The transform formula for ideals 111
Notes 120
vii
viii CONTENTS
Chapter V. Generalized Dedekind Domains 125
5.1. Localizing systems 125
5.2. Generalized Dedekind domains 143
5.3. Strongly discrete Priifer domains 144
5.4. Characterizing generalized Dedekind domains 150
5.5. Generalized Dedekind domains and property (#p) 156
5.6. Generalized Dedekind domains and field extensions 159
5.7. Generalized Dedekind domains and pullbacks 165
5.8. Generalized Dedekind domains with torsion class group 167
Notes 178
Chapter VI. Polynomial Extensions and Quasi-Priifer Domains 183
6.1. Divisorial ideals in polynomial rings 184
6.2. Applications: G-GCD domains and domains satisfying KP 188
6.3. Universally catenarian domains 196
6.4. Projective modules over polynomial rings with Priifer coefficients 206
6.5. Quasi-Priifer domains 212
6.6 Incomparability and polynomial extensions 231
6.7. Quasi-Priifer domains, Jaffard domains and strong S-domains 236
Notes 243
Chapter VII. Additional Topics 249
7.1. Absolute non-zero-divisors 249
7.2. Ao-extensions 257
7.3. Stability 262
7.4. Quasi-Priifer domains and stability 265
Notes 271
Chapter VIII. Constructions and Examples 275
8.1. The ring of entire functions 275
8.2. An almost Dedekind domain 280
CONTENTS ix
8.3. The Priifer domain PX(R) 285
8.4. Examples 293
Notes 309
Bibliography 311
Index 325
|
| any_adam_object | 1 |
| author | Fontana, Marco 1947- Huckaba, James A. Papick, Ira J. |
| author_GND | (DE-588)139350543 |
| author_facet | Fontana, Marco 1947- Huckaba, James A. Papick, Ira J. |
| author_role | aut aut aut |
| author_sort | Fontana, Marco 1947- |
| author_variant | m f mf j a h ja jah i j p ij ijp |
| building | Verbundindex |
| bvnumber | BV011097255 |
| callnumber-first | Q - Science |
| callnumber-label | QA247 |
| callnumber-raw | QA247 |
| callnumber-search | QA247 |
| callnumber-sort | QA 3247 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)35095951 (DE-599)BVBBV011097255 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| 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>02447nam a2200421 cb4500</leader><controlfield tag="001">BV011097255</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20091203 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">961204s1997 xx |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0824798163</subfield><subfield code="9">0-8247-9816-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)35095951</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011097255</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-355</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA247</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.4</subfield><subfield code="2">20</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">Fontana, Marco</subfield><subfield code="d">1947-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)139350543</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Prüfer domains</subfield><subfield code="c">Marco Fontana ; James A. Huckaba ; Ira J. Papick</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Dekker</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 328 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="1" ind2=" "><subfield code="a">Pure and applied mathematics</subfield><subfield code="v">203</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">This timely reference offers - for the first time in book form - an exhaustive examination of many important developments in the theory of Prufer domains that have occurred over the past 25 years. Providing an integrated presentation of both research advances and analysis techniques, Prufer Domains covers the solution of the problem of finding the number of generators needed for a finitely generated ideal of a Prufer domain... concrete representations of particular overrings determined by ideals of R...various recently developed trace properties...polynomial rings over Prufer domains... extensions and generalizations of the originals theory...and more. Written by three acknowledged experts in the field, Prufer Domains is an excellent resource for pure and applied mathematicians, particularly algebraists and number theorists, and upper-level undergraduate and graduate students in the disciplines.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Anneaux (algèbre)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Prüfer rings</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Prüfer-Ring</subfield><subfield code="0">(DE-588)4520857-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Prüfer-Ring</subfield><subfield code="0">(DE-588)4520857-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Huckaba, James A.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Papick, Ira J.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Pure and applied mathematics</subfield><subfield code="v">203</subfield><subfield code="w">(DE-604)BV000001885</subfield><subfield code="9">203</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=007434145&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:BVB01-007434145</subfield></datafield></record></collection> |
| id | DE-604.BV011097255 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:06:14Z |
| institution | BVB |
| isbn | 0824798163 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007434145 |
| oclc_num | 35095951 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-739 DE-12 DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-739 DE-12 DE-703 |
| physical | IX, 328 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spellingShingle | Fontana, Marco 1947- Huckaba, James A. Papick, Ira J. Prüfer domains Pure and applied mathematics Anneaux (algèbre) ram Prüfer rings Prüfer-Ring (DE-588)4520857-8 gnd |
| subject_GND | (DE-588)4520857-8 |
| title | Prüfer domains |
| title_auth | Prüfer domains |
| title_exact_search | Prüfer domains |
| title_full | Prüfer domains Marco Fontana ; James A. Huckaba ; Ira J. Papick |
| title_fullStr | Prüfer domains Marco Fontana ; James A. Huckaba ; Ira J. Papick |
| title_full_unstemmed | Prüfer domains Marco Fontana ; James A. Huckaba ; Ira J. Papick |
| title_short | Prüfer domains |
| title_sort | prufer domains |
| topic | Anneaux (algèbre) ram Prüfer rings Prüfer-Ring (DE-588)4520857-8 gnd |
| topic_facet | Anneaux (algèbre) Prüfer rings Prüfer-Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007434145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT fontanamarco pruferdomains AT huckabajamesa pruferdomains AT papickiraj pruferdomains |