MARC details
| 000 -LEADER |
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| fixed length control field |
02271nmm a22002775i 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20230705150643.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
130409s2001 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783662046487 |
| -- |
978-3-662-04648-7 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
512 |
| Edition number |
23 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Prestel, Alexander. |
| 9 (RLIN) |
20800 |
| 245 ## - TITLE STATEMENT |
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| Title |
Positive Polynomials |
| Medium |
[electronic resource] : |
| Remainder of title |
From Hilbert's 17th Problem to Real Algebra / |
| Statement of responsibility, etc. |
by Alexander Prestel, Charles Delzell. |
| 250 ## - EDITION STATEMENT |
|---|
| Edition statement |
1st ed. 2001. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
Berlin, Heidelberg : |
| Name of publisher, distributor, etc. |
Springer Berlin Heidelberg : |
| -- |
Imprint: Springer, |
| Date of publication, distribution, etc. |
2001. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
VIII, 268 p. |
| Other physical details |
online resource. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. Real Fields -- 2. Semialgebraic Sets -- 3. Quadratic Forms over Real Fields -- 4. Real Rings -- 5. Archimedean Rings -- 6. Positive Polynomials on Semialgebraic Sets -- 7. Sums of 2mth Powers -- 8. Bounds -- Appendix: Valued Fields -- A.1 Valuations -- A.2 Algebraic Extensions -- A.3 Henselian Fields -- A.4 Complete Fields -- A.5 Dependence and Composition of Valuations -- A.6 Transcendental Extensions -- A.7 Exercises -- A.8 Bibliographical Comments -- References -- Glossary of Notations. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc. |
Positivity is one of the most basic mathematical concepts. In many areas of mathematics (like analysis, real algebraic geometry, functional analysis, etc.) it shows up as positivity of a polynomial on a certain subset of R^n which itself is often given by polynomial inequalities. The main objective of the book is to give useful characterizations of such polynomials. It takes as starting point Hilbert's 17th Problem from 1900 and explains how E. Artin's solution of that problem eventually led to the development of real algebra towards the end of the 20th century. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed. Thus the monograph can also serve as the basis for a 2-semester course in real algebra. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Algebra. |
| 9 (RLIN) |
20801 |
|
|---|
| Topical term or geographic name entry element |
Algebraic geometry. |
| 9 (RLIN) |
20802 |
|
|---|
| Topical term or geographic name entry element |
Functional analysis. |
| 9 (RLIN) |
20803 |
|
|---|
| Topical term or geographic name entry element |
Algebra. |
| 9 (RLIN) |
20801 |
|
|---|
| Topical term or geographic name entry element |
Algebraic Geometry. |
| 9 (RLIN) |
20804 |
|
|---|
| Topical term or geographic name entry element |
Functional Analysis. |
| 9 (RLIN) |
20805 |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Delzell, Charles. |
| Relator term |
author. |
| Relationship |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) |
20806 |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-3-662-04648-7">https://doi.org/10.1007/978-3-662-04648-7</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Koha item type |
e-Book |
