Topics in ĉ-adic Topologies:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1971
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
58 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The m-adic topologies and, in particular the notions of m-complete ring and m-completion A of a commutative ring A, occur frequently in commutative algebra and are also a useful tool in algebraic geometry. The aim of this work is to collect together some criteria concerning the ascent (from A to A) and the descent (from A to A) of several properties of commutative rings such as, for example: integrity, regularity, factoriality, normality, etc. More precisely, we want to show that many of the above criteria, although not trivial at all, are elementary consequences of some fundamental notions of commutative algebra and local algebra. Sometimes we are able to get only partial results, which probably can be improved by further deeper investigations. No new result has been included in this work. Its only origi nality is the choice of material and the mode of presentation. The comprehension of the most important statements included in this book needs only a very elementary background in algebra, ideal theory and general topology. In order to emphasize the elementary character of our treatment, we have recalled several well known definitions and, sometimes, even the proofs of the first properties which follow directly from them. On the other hand, we did not insert in this work some important results, such as the Cohen structure theorem on complete noetherian local rings, as we did not want to get away too much from the spirit of the book |
| Beschreibung: | 1 Online-Ressource (VII, 76 p) |
| ISBN: | 9783642885013 9783642885037 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-88501-3 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423098 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1971 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642885013 |c Online |9 978-3-642-88501-3 | ||
| 020 | |a 9783642885037 |c Print |9 978-3-642-88503-7 | ||
| 024 | 7 | |a 10.1007/978-3-642-88501-3 |2 doi | |
| 035 | |a (OCoLC)863980238 | ||
| 035 | |a (DE-599)BVBBV042423098 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Greco, Silvio |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topics in ĉ-adic Topologies |c by Silvio Greco, Paolo Salmon |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1971 | |
| 300 | |a 1 Online-Ressource (VII, 76 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 58 |x 0071-1136 | |
| 500 | |a The m-adic topologies and, in particular the notions of m-complete ring and m-completion A of a commutative ring A, occur frequently in commutative algebra and are also a useful tool in algebraic geometry. The aim of this work is to collect together some criteria concerning the ascent (from A to A) and the descent (from A to A) of several properties of commutative rings such as, for example: integrity, regularity, factoriality, normality, etc. More precisely, we want to show that many of the above criteria, although not trivial at all, are elementary consequences of some fundamental notions of commutative algebra and local algebra. Sometimes we are able to get only partial results, which probably can be improved by further deeper investigations. No new result has been included in this work. Its only origi nality is the choice of material and the mode of presentation. The comprehension of the most important statements included in this book needs only a very elementary background in algebra, ideal theory and general topology. In order to emphasize the elementary character of our treatment, we have recalled several well known definitions and, sometimes, even the proofs of the first properties which follow directly from them. On the other hand, we did not insert in this work some important results, such as the Cohen structure theorem on complete noetherian local rings, as we did not want to get away too much from the spirit of the book | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Salmon, Paolo |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-88501-3 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858515 | ||
Datensatz im Suchindex
| _version_ | 1804153098444210176 |
|---|---|
| any_adam_object | |
| author | Greco, Silvio |
| author_facet | Greco, Silvio |
| author_role | aut |
| author_sort | Greco, Silvio |
| author_variant | s g sg |
| building | Verbundindex |
| bvnumber | BV042423098 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863980238 (DE-599)BVBBV042423098 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-88501-3 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02784nmm a2200409zcb4500</leader><controlfield tag="001">BV042423098</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1971 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642885013</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-88501-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642885037</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-88503-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-88501-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863980238</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423098</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Greco, Silvio</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Topics in ĉ-adic Topologies</subfield><subfield code="c">by Silvio Greco, Paolo Salmon</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1971</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VII, 76 p)</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">Ergebnisse der Mathematik und ihrer Grenzgebiete</subfield><subfield code="v">58</subfield><subfield code="x">0071-1136</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The m-adic topologies and, in particular the notions of m-complete ring and m-completion A of a commutative ring A, occur frequently in commutative algebra and are also a useful tool in algebraic geometry. The aim of this work is to collect together some criteria concerning the ascent (from A to A) and the descent (from A to A) of several properties of commutative rings such as, for example: integrity, regularity, factoriality, normality, etc. More precisely, we want to show that many of the above criteria, although not trivial at all, are elementary consequences of some fundamental notions of commutative algebra and local algebra. Sometimes we are able to get only partial results, which probably can be improved by further deeper investigations. No new result has been included in this work. Its only origi nality is the choice of material and the mode of presentation. The comprehension of the most important statements included in this book needs only a very elementary background in algebra, ideal theory and general topology. In order to emphasize the elementary character of our treatment, we have recalled several well known definitions and, sometimes, even the proofs of the first properties which follow directly from them. On the other hand, we did not insert in this work some important results, such as the Cohen structure theorem on complete noetherian local rings, as we did not want to get away too much from the spirit of the book</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Salmon, Paolo</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-88501-3</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858515</subfield></datafield></record></collection> |
| id | DE-604.BV042423098 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642885013 9783642885037 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858515 |
| oclc_num | 863980238 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VII, 76 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Greco, Silvio Verfasser aut Topics in ĉ-adic Topologies by Silvio Greco, Paolo Salmon Berlin, Heidelberg Springer Berlin Heidelberg 1971 1 Online-Ressource (VII, 76 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 58 0071-1136 The m-adic topologies and, in particular the notions of m-complete ring and m-completion A of a commutative ring A, occur frequently in commutative algebra and are also a useful tool in algebraic geometry. The aim of this work is to collect together some criteria concerning the ascent (from A to A) and the descent (from A to A) of several properties of commutative rings such as, for example: integrity, regularity, factoriality, normality, etc. More precisely, we want to show that many of the above criteria, although not trivial at all, are elementary consequences of some fundamental notions of commutative algebra and local algebra. Sometimes we are able to get only partial results, which probably can be improved by further deeper investigations. No new result has been included in this work. Its only origi nality is the choice of material and the mode of presentation. The comprehension of the most important statements included in this book needs only a very elementary background in algebra, ideal theory and general topology. In order to emphasize the elementary character of our treatment, we have recalled several well known definitions and, sometimes, even the proofs of the first properties which follow directly from them. On the other hand, we did not insert in this work some important results, such as the Cohen structure theorem on complete noetherian local rings, as we did not want to get away too much from the spirit of the book Mathematics Mathematics, general Mathematik Salmon, Paolo Sonstige oth https://doi.org/10.1007/978-3-642-88501-3 Verlag Volltext |
| spellingShingle | Greco, Silvio Topics in ĉ-adic Topologies Mathematics Mathematics, general Mathematik |
| title | Topics in ĉ-adic Topologies |
| title_auth | Topics in ĉ-adic Topologies |
| title_exact_search | Topics in ĉ-adic Topologies |
| title_full | Topics in ĉ-adic Topologies by Silvio Greco, Paolo Salmon |
| title_fullStr | Topics in ĉ-adic Topologies by Silvio Greco, Paolo Salmon |
| title_full_unstemmed | Topics in ĉ-adic Topologies by Silvio Greco, Paolo Salmon |
| title_short | Topics in ĉ-adic Topologies |
| title_sort | topics in c adic topologies |
| topic | Mathematics Mathematics, general Mathematik |
| topic_facet | Mathematics Mathematics, general Mathematik |
| url | https://doi.org/10.1007/978-3-642-88501-3 |
| work_keys_str_mv | AT grecosilvio topicsincadictopologies AT salmonpaolo topicsincadictopologies |