The classical fields: structural features of the real and rational numbers
The classical fields are the real, rational, complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive volume analyzes the interaction and interdependencies of these different aspects. The real and rational num...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo
Cambridge University Press
[2007]
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 112 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UPA01 Volltext |
| Zusammenfassung: | The classical fields are the real, rational, complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive volume analyzes the interaction and interdependencies of these different aspects. The real and rational numbers are examined additionally with respect to their orderings, and these fields are compared to their non-standard counterparts. Typical substructures and quotients, relevant automorphism groups and many counterexamples are described. Also discussed are completion procedures of chains and of ordered and topological groups, with applications to classical fields. The p-adic numbers are placed in the context of general topological fields: absolute values, valuations and the corresponding topologies are studied, and the classification of all locally compact fields and skew fields is presented. Exercises are provided with hints and solutions at the end of the book. An appendix reviews ordinals and cardinals, duality theory of locally compact Abelian groups and various constructions of fields |
| Beschreibung: | 1 online resource (xv, 401 pages) |
| ISBN: | 9780511721502 |
| DOI: | 10.1017/CBO9780511721502 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043941274 | ||
| 003 | DE-604 | ||
| 005 | 20220913 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2007 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511721502 |c Online |9 978-0-511-72150-2 | ||
| 024 | 7 | |a 10.1017/CBO9780511721502 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511721502 | ||
| 035 | |a (OCoLC)967600480 | ||
| 035 | |a (DE-599)BVBBV043941274 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-739 | ||
| 082 | 0 | |a 512.74 |2 22 | |
| 100 | 1 | |a Salzmann, Helmut R. |d 1930-2022 |e Verfasser |0 (DE-588)14099839X |4 aut | |
| 245 | 1 | 0 | |a The classical fields |b structural features of the real and rational numbers |c H. Salzmann [and others] |
| 264 | 1 | |a Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo |b Cambridge University Press |c [2007] | |
| 264 | 4 | |c © 2007 | |
| 300 | |a 1 online resource (xv, 401 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Encyclopedia of mathematics and its applications |v volume 112 | |
| 520 | |a The classical fields are the real, rational, complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive volume analyzes the interaction and interdependencies of these different aspects. The real and rational numbers are examined additionally with respect to their orderings, and these fields are compared to their non-standard counterparts. Typical substructures and quotients, relevant automorphism groups and many counterexamples are described. Also discussed are completion procedures of chains and of ordered and topological groups, with applications to classical fields. The p-adic numbers are placed in the context of general topological fields: absolute values, valuations and the corresponding topologies are studied, and the classification of all locally compact fields and skew fields is presented. Exercises are provided with hints and solutions at the end of the book. An appendix reviews ordinals and cardinals, duality theory of locally compact Abelian groups and various constructions of fields | ||
| 650 | 4 | |a Numbers, Real | |
| 650 | 4 | |a Numbers, Rational | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Rationale Zahl |0 (DE-588)4048495-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Reelle Zahl |0 (DE-588)4202628-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Struktur |g Mathematik |0 (DE-588)4183783-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Reelle Zahl |0 (DE-588)4202628-3 |D s |
| 689 | 0 | 1 | |a Rationale Zahl |0 (DE-588)4048495-6 |D s |
| 689 | 0 | 2 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | 3 | |a Struktur |g Mathematik |0 (DE-588)4183783-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Hardcover |z 978-0-521-86516-6 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511721502 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029350245 | ||
| 966 | e | |u https://doi.org/10.1017/CBO9780511721502 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511721502 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511721502 |l UPA01 |p ZDB-20-CBO |q UPA_PDA_CBO_Kauf2021 |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176882727387136 |
|---|---|
| any_adam_object | |
| author | Salzmann, Helmut R. 1930-2022 |
| author_GND | (DE-588)14099839X |
| author_facet | Salzmann, Helmut R. 1930-2022 |
| author_role | aut |
| author_sort | Salzmann, Helmut R. 1930-2022 |
| author_variant | h r s hr hrs |
| building | Verbundindex |
| bvnumber | BV043941274 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511721502 (OCoLC)967600480 (DE-599)BVBBV043941274 |
| dewey-full | 512.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.74 |
| dewey-search | 512.74 |
| dewey-sort | 3512.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511721502 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03393nmm a2200541zcb4500</leader><controlfield tag="001">BV043941274</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220913 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2007 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511721502</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-72150-2</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511721502</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511721502</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)967600480</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941274</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-739</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.74</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Salzmann, Helmut R.</subfield><subfield code="d">1930-2022</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)14099839X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The classical fields</subfield><subfield code="b">structural features of the real and rational numbers</subfield><subfield code="c">H. Salzmann [and others]</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">[2007]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xv, 401 pages)</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Encyclopedia of mathematics and its applications</subfield><subfield code="v">volume 112</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The classical fields are the real, rational, complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive volume analyzes the interaction and interdependencies of these different aspects. The real and rational numbers are examined additionally with respect to their orderings, and these fields are compared to their non-standard counterparts. Typical substructures and quotients, relevant automorphism groups and many counterexamples are described. Also discussed are completion procedures of chains and of ordered and topological groups, with applications to classical fields. The p-adic numbers are placed in the context of general topological fields: absolute values, valuations and the corresponding topologies are studied, and the classification of all locally compact fields and skew fields is presented. Exercises are provided with hints and solutions at the end of the book. An appendix reviews ordinals and cardinals, duality theory of locally compact Abelian groups and various constructions of fields</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Numbers, Real</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Numbers, Rational</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Rationale Zahl</subfield><subfield code="0">(DE-588)4048495-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Reelle Zahl</subfield><subfield code="0">(DE-588)4202628-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Struktur</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4183783-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Reelle Zahl</subfield><subfield code="0">(DE-588)4202628-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Rationale Zahl</subfield><subfield code="0">(DE-588)4048495-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Struktur</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4183783-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Hardcover</subfield><subfield code="z">978-0-521-86516-6</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511721502</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350245</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511721502</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511721502</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511721502</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UPA_PDA_CBO_Kauf2021</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043941274 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:15Z |
| institution | BVB |
| isbn | 9780511721502 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350245 |
| oclc_num | 967600480 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-739 |
| owner_facet | DE-12 DE-92 DE-739 |
| physical | 1 online resource (xv, 401 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UPA_PDA_CBO_Kauf2021 |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Salzmann, Helmut R. 1930-2022 Verfasser (DE-588)14099839X aut The classical fields structural features of the real and rational numbers H. Salzmann [and others] Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo Cambridge University Press [2007] © 2007 1 online resource (xv, 401 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 112 The classical fields are the real, rational, complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive volume analyzes the interaction and interdependencies of these different aspects. The real and rational numbers are examined additionally with respect to their orderings, and these fields are compared to their non-standard counterparts. Typical substructures and quotients, relevant automorphism groups and many counterexamples are described. Also discussed are completion procedures of chains and of ordered and topological groups, with applications to classical fields. The p-adic numbers are placed in the context of general topological fields: absolute values, valuations and the corresponding topologies are studied, and the classification of all locally compact fields and skew fields is presented. Exercises are provided with hints and solutions at the end of the book. An appendix reviews ordinals and cardinals, duality theory of locally compact Abelian groups and various constructions of fields Numbers, Real Numbers, Rational Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Rationale Zahl (DE-588)4048495-6 gnd rswk-swf Reelle Zahl (DE-588)4202628-3 gnd rswk-swf Struktur Mathematik (DE-588)4183783-6 gnd rswk-swf Reelle Zahl (DE-588)4202628-3 s Rationale Zahl (DE-588)4048495-6 s Zahlentheorie (DE-588)4067277-3 s Struktur Mathematik (DE-588)4183783-6 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-0-521-86516-6 https://doi.org/10.1017/CBO9780511721502 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Salzmann, Helmut R. 1930-2022 The classical fields structural features of the real and rational numbers Numbers, Real Numbers, Rational Number theory Zahlentheorie (DE-588)4067277-3 gnd Rationale Zahl (DE-588)4048495-6 gnd Reelle Zahl (DE-588)4202628-3 gnd Struktur Mathematik (DE-588)4183783-6 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4048495-6 (DE-588)4202628-3 (DE-588)4183783-6 |
| title | The classical fields structural features of the real and rational numbers |
| title_auth | The classical fields structural features of the real and rational numbers |
| title_exact_search | The classical fields structural features of the real and rational numbers |
| title_full | The classical fields structural features of the real and rational numbers H. Salzmann [and others] |
| title_fullStr | The classical fields structural features of the real and rational numbers H. Salzmann [and others] |
| title_full_unstemmed | The classical fields structural features of the real and rational numbers H. Salzmann [and others] |
| title_short | The classical fields |
| title_sort | the classical fields structural features of the real and rational numbers |
| title_sub | structural features of the real and rational numbers |
| topic | Numbers, Real Numbers, Rational Number theory Zahlentheorie (DE-588)4067277-3 gnd Rationale Zahl (DE-588)4048495-6 gnd Reelle Zahl (DE-588)4202628-3 gnd Struktur Mathematik (DE-588)4183783-6 gnd |
| topic_facet | Numbers, Real Numbers, Rational Number theory Zahlentheorie Rationale Zahl Reelle Zahl Struktur Mathematik |
| url | https://doi.org/10.1017/CBO9780511721502 |
| work_keys_str_mv | AT salzmannhelmutr theclassicalfieldsstructuralfeaturesoftherealandrationalnumbers |