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| 001 - CONTROL NUMBER |
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11311577 |
| 003 - CONTROL NUMBER IDENTIFIER |
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OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20200728114901.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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121227s1964 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780387942933 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-1-4612-9872-4 |
| Source of number or code |
doi |
| Terms of availability |
6310.00 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(WaSeSS)ssj0001297358 |
| 040 ## - CATALOGING SOURCE |
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| Modifying agency |
WaSeSS |
| Transcribing agency |
AUI |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA1-939 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PB |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
|---|
| Subject category code |
MAT000000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Edition number |
23 |
| Classification number |
512.24 |
| Item number |
EIS |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Eisenbud David |
| Relator term |
author. |
| 9 (RLIN) |
6029 |
| 245 10 - TITLE STATEMENT |
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| Title |
Graduate Texts In Mathematics |
| Remainder of title |
Commutative Algebra with a view Toward Algebaraic Geometry |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
2nd.ed |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
New York |
| Name of publisher, distributor, etc. |
Springer |
| Date of publication, distribution, etc. |
1994. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
vii;235 p. |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Graduate Texts in Mathematics, |
| International Standard Serial Number |
0072-5285 ; |
| Volume/sequential designation |
32 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. Extension of homomorphisms -- 2. Algebras -- 3. Tensor products of vector spaces -- 4. Tensor product of algebras -- I: Finite Dimensional Extension Fields -- 1. Some vector spaces associated with mappings of fields -- 2. The Jacobson-Bourbaki correspondence -- 3. Dedekind independence theorem for isomorphisms of a field -- 4. Finite groups of automorphisms -- 5. Splitting field of a polynomial -- 6. Multiple roots. Separable polynomials -- 7. The 'fundamental theorem' of Galois theory -- 8. Normal extensions. Normal closures -- 9. Structure of algebraic extensions. Separability -- 10. Degrees of separability and inseparability. Structure of normal extensions -- 11. Primitive elements -- 12. Normal bases -- 13 Finite fields -- 14. Regular representation, trace and norm -- 15. Galois cohomology -- 16 Composites of fields -- II: Galois Theory of Equations -- 1. The Galois group of an equation -- 2. Pure equations -- 3. Galois' criterion for solvability by radicals -- 4. The general equation of n-th degree -- 5. Equations with rational coefficients and symmetric group as Galois group -- III: Abelian Extensions -- 1. Cyclotomic fields over the rationals -- 2. Characters of finite commutative groups -- 3. Kummer extensions -- 4. Witt vectors -- 5. Abelian p-extensions -- IV: Structure Theory of Fields -- 1. Algebraically closed fields -- 2. Infinite Galois theory -- 3. Transcendency basis -- 4. L�roth's theorem -- 5. Linear disjointness and separating transcendency bases -- 6. Derivations -- 7. Derivations, separability and p-independence -- 8. Galois theory for purely inseparable extensions of exponent one -- 9. Higher derivations -- 10. Tensor products of fields -- 11. Free composites of fields -- V: Valuation Theory -- 1. Real valuations -- 2. Real valuations of the field of rational numbers -- 3. Real valuations of ?(x) which are trivial in ? -- 4. Completion of a field -- 5. Some properties of the field of p-adic numbers -- 6. Hensel's lemma -- 7. Construction of complete fields with given residue fields -- 8. Ordered groups and valuations -- 9. Valuations, valuation rings, and places -- 10. Characterization of real non-archimedean valuations -- 11. Extension of homomorphisms and valuations -- 12. Application of the extension theorem: Hilbert Nullstellensatz -- 13. Application of the extension theorem: integral closure -- 14. Finite dimensional extensions of complete fields -- 15. Extension of real valuations to finite dimensional extension fields -- 16. Ramification index and residue degree -- VI: Artin-Schreier Theory -- 1. Ordered fields and formally real fields -- 2. Real closed fields -- 3. Sturm's theorem -- 4. Real closure of an ordered field -- 5. Real algebraic numbers -- 6. Positive definite rational functions -- 7. Formalization of Sturm's theorem. Resultants -- 8. Decision method for an algebraic curve -- 9. Equations with parameters -- 10. Generalized Sturm's theorem. Applications -- 11. Artin-Schreier characterization of real closed fields -- Suggestions for further reading. |
| 506 ## - RESTRICTIONS ON ACCESS NOTE |
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| Terms governing access |
License restrictions may limit access. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a number of objectives in mind. First and foremost has been that of presenting the basic field theory which is essential for an understanding of modern algebraic number theory, ring theory, and algebraic geometry. The parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen sional field extensions and Galois theory, general structure theory of fields, and valuation theory. Also the results of Chapter IlIon abelian extensions, although of a somewhat specialized nature, are of interest in number theory. A second objective of our ac count has been to indicate the links between the present theory of fields and the classical problems which led to its development. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 9 (RLIN) |
6030 |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematics. |
| 9 (RLIN) |
6031 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematics, general. |
| 9 (RLIN) |
6032 |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 9 (RLIN) |
6033 |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 773 #0 - HOST ITEM ENTRY |
|---|
| Title |
SpringerLink ebooks - Mathematics and Statistics (Archive) |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Printed edition: |
| International Standard Book Number |
9780387901244 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Graduate Texts in Mathematics, |
| Volume/sequential designation |
32 |
| 9 (RLIN) |
6034 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
<a href="http://www.columbia.edu/cgi-bin/cul/resolve?clio11311577">http://www.columbia.edu/cgi-bin/cul/resolve?clio11311577</a> |
| Public note |
Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive) |
| 910 ## - USER-OPTION DATA (OCLC) |
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| User-option data |
Vendor-generated brief record |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Book |
| 990 ## - EQUIVALENCES OR CROSS-REFERENCES [LOCAL, CANADA] |
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| Link information for 9XX fields |
QA |
