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02851nam a22004575i 4500 |
| 001 - CONTROL NUMBER |
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978-3-319-03212-2 |
| 003 - CONTROL NUMBER IDENTIFIER |
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DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20150803155057.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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140320s2014 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319032122 |
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978-3-319-03212-2 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-3-319-03212-2 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA251.3 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBF |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT002010 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.44 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Knebusch, Manfred. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Manis Valuations and Prüfer Extensions II |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Manfred Knebusch, Tobias Kaiser. |
| 264 #1 - |
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| -- |
Cham : |
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Springer International Publishing : |
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Imprint: Springer, |
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2014. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XII, 190 p. |
| Other physical details |
online resource. |
| 336 ## - |
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text |
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txt |
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rdacontent |
| 337 ## - |
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computer |
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c |
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rdamedia |
| 338 ## - |
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online resource |
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cr |
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rdacarrier |
| 347 ## - |
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text file |
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PDF |
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rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Lecture Notes in Mathematics, |
| International Standard Serial Number |
0075-8434 ; |
| Volume number/sequential designation |
2103 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Overrings and PM-Spectra -- Approximation Theorems -- Kronecker extensions and star operations -- Basics on Manis valuations and Prufer extensions -- Multiplicative ideal theory -- PM-valuations and valuations of weaker type -- Overrings and PM-Spectra -- Approximation Theorems -- Kronecker extensions and star operations -- Appendix -- References -- Index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This volume is a sequel to “Manis Valuation and Prüfer Extensions I,” LNM1791. The Prüfer extensions of a commutative ring A are roughly those commutative ring extensions R / A,where commutative algebra is governed by Manis valuations on R with integral values on A. These valuations then turn out to belong to the particularly amenable subclass of PM (=Prüfer-Manis) valuations. While in Volume I Prüfer extensions in general and individual PM valuations were studied, now the focus is on families of PM valuations. One highlight is the presentation of a very general and deep approximation theorem for PM valuations, going back to Joachim Gräter’s work in 1980, a far-reaching extension of the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called “Kronecker extensions,” where PM valuations are put to use in arbitrary commutative ring extensions in a way that ultimately goes back to the work of Leopold Kronecker. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Commutative Rings and Algebras. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Kaiser, Tobias. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9783319032115 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Lecture Notes in Mathematics, |
| -- |
0075-8434 ; |
| Volume number/sequential designation |
2103 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-319-03212-2 |
| 912 ## - |
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ZDB-2-SMA |
| 912 ## - |
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ZDB-2-LNM |
