MARC details
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05891cam a2200805 a 4500 |
| 001 - CONTROL NUMBER |
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ocn836870322 |
| 003 - CONTROL NUMBER IDENTIFIER |
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OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20220711195015.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION |
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m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr cnu---unuuu |
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130408s1993 enk ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
N$T |
| Language of cataloging |
eng |
| Description conventions |
pn |
| Transcribing agency |
N$T |
| Modifying agency |
E7B |
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OCLCO |
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COO |
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OCLCF |
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YDXCP |
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OCLCQ |
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AGLDB |
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HEBIS |
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OCLCO |
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UAB |
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OCLCQ |
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VTS |
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OCLCA |
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REC |
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OCLCO |
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M8D |
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OCLCO |
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SFB |
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OCLCQ |
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OCLCO |
| 019 ## - |
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797839839 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781107362031 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1107362032 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
0521458862 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
9780521458863 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
9780511565809 |
| 029 1# - (OCLC) |
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| OCLC library identifier |
DEBBG |
| System control number |
BV043083237 |
| 029 1# - (OCLC) |
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| OCLC library identifier |
DEBSZ |
| System control number |
421267143 |
| 029 1# - (OCLC) |
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| OCLC library identifier |
GBVCP |
| System control number |
804535264 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)836870322 |
| Canceled/invalid control number |
(OCoLC)797839839 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA201 |
| Item number |
.B46 1993eb |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
002050 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512./5 |
| Edition number |
22 |
| 084 ## - OTHER CLASSIFICATION NUMBER |
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| Classification number |
31.21 |
| Source of number |
bcl |
| 049 ## - LOCAL HOLDINGS (OCLC) |
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| Holding library |
MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Benson, D. J. |
| Fuller form of name |
(David J.), |
| Dates associated with a name |
1955- |
| 9 (RLIN) |
937937 |
| 245 10 - TITLE STATEMENT |
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| Title |
Polynomial invariants of finite groups / |
| Statement of responsibility, etc |
D.J. Benson. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Cambridge ; |
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New York : |
| Name of publisher, distributor, etc |
Cambridge University Press, |
| Date of publication, distribution, etc |
©1993. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource (ix, 118 pages) |
| 336 ## - |
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text |
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txt |
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rdacontent |
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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 |
| 490 1# - SERIES STATEMENT |
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| Series statement |
London Mathematical Society lecture note series ; |
| Volume number/sequential designation |
190 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references (pages 109-115) and index. |
| 588 0# - |
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| -- |
Print version record. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This is the first book to deal with invariant theory and the representations of finite groups. By restricting attention to finite groups Dr Benson is able to avoid recourse to the technical machinery of algebraic groups, and he develops the necessary results from commutative algebra as he proceeds. Thus the book should be accessible to graduate students. In detail, the book contains an account of invariant theory for the action of a finite group on the ring of polynomial functions on a linear representation, both in characteristic zero and characteristic p. Special attention is paid to the role played by pseudoreflections, which arise because they correspond to the divisors in the polynomial ring which ramify over the invariants. Also included is a new proof by Crawley-Boevey and the author of the Carlisle-Kropholler conjecture. This volume will appeal to all algebraists, but especially those working in representation theory, group theory, and commutative or homological algebra. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Cover; Title; Contents; Introduction; 1 Finite Generation of Invariants; 1.1 The basic object of study; 1.2 Noetherian rings and modules; 1.3 Finite groups in arbitrary characteristic; 1.4 Krull dimension and going up and down; 1.5 Noether's bound in characteristic zero; 1.6 Linearly reductive algebraic groups; 2 Poincare series; 2.1 The Hilbert-Serre theorem; 2.2 Noether normalization; 2.3 Systems of parameters; 2.4 Degree and if>; 2.5 Molien's theorem; 2.6 Reflecting hyperplanes; 3 Divisor Classes, Ramification and Hyperplanes; 3.1 Divisors; 3.2 Primes of height one; 3.3 Duality |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
3.4 Reflexive modules3.5 Divisor classes and unique factorization; 3.6 The Picard group; 3.7 The trace; 3.8 Ramification; 3.9 Cl(ii:[V]G); 3.10 The different; 3.11 The homological different; 3.12 A ramification formula; 3.13 The Carlisle-Kropholler conjecture; 4 Homological Properties of Invariants; 4.1 Minimal resolutions; 4.2 Hilbert's syzygy theorem; 4.3 Depth and Cohen-Macaulay rings; 4.4 Homological characterization of depth; 4.5 The canonical module and Gorenstein rings; 4.6 Watanabe's theorem; 5 Polynomial tensor exterior algebras; 5.1 Motivation and first properties |
| 505 8# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
5.2 A variation on Molien's theorem5.3 The invariants are graded Gorenstein; 5.4 The Jacobian; 6 Polynomial rings and regular local rings; 6.1 Regular local rings; 6.2 Serre's converse to Hilbert's syzygy theorem; 6.3 Uniqueness of factorization; 6.4 Reflexive modules; 7 Groups Generated by Pseudoreflections; 7.1 Reflections and pseudoreflections; 7.2 The Shephard-Todd theorem; 7.3 A theorem of Solomon; 8 Modular invariants; 8.1 Dickson's theorem; 8.2 The special linear group; 8.3 Symplectic invariants; A Examples over the complex numbers; B Examples over finite fields; Bibliography; Index |
| 590 ## - LOCAL NOTE (RLIN) |
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| Local note |
eBooks on EBSCOhost |
| Provenance (VM) [OBSOLETE] |
EBSCO eBook Subscription Academic Collection - Worldwide |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Invariants. |
| 9 (RLIN) |
196046 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Finite groups. |
| 9 (RLIN) |
119864 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Divisor theory. |
| 9 (RLIN) |
664738 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Invariants. |
| 9 (RLIN) |
196046 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Groupes finis. |
| 9 (RLIN) |
907904 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Théorie des diviseurs. |
| 9 (RLIN) |
937938 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Algebra |
| -- |
Linear. |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
869416 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Divisor theory. |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst00895808 |
| 9 (RLIN) |
664738 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Finite groups. |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst00924908 |
| 9 (RLIN) |
119864 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Invariants. |
| Source of heading or term |
fast |
| -- |
(OCoLC)fst00977982 |
| 9 (RLIN) |
196046 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Endliche Gruppe |
| Source of heading or term |
gnd |
| 9 (RLIN) |
907905 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Invariante |
| Source of heading or term |
gnd |
| 9 (RLIN) |
918778 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Invariantentheorie |
| Source of heading or term |
gnd |
| 9 (RLIN) |
933764 |
| 650 17 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Eindige groepen. |
| Source of heading or term |
gtt |
| 9 (RLIN) |
937376 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Invariants. |
| Source of heading or term |
ram |
| 9 (RLIN) |
196046 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Groupes finis. |
| Source of heading or term |
ram |
| 9 (RLIN) |
907904 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Diviseurs, Théorie des. |
| Source of heading or term |
ram |
| 9 (RLIN) |
937939 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Groupes de classes (Mathématiques) |
| Source of heading or term |
ram |
| 9 (RLIN) |
937940 |
| 653 0# - INDEX TERM--UNCONTROLLED |
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| Uncontrolled term |
Groups (Mathematics) |
| 655 #4 - INDEX TERM--GENRE/FORM |
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| Genre/form data or focus term |
Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Print version: |
| Main entry heading |
Benson, D.J. (David J.), 1955- |
| Title |
Polynomial invariants of finite groups. |
| Place, publisher, and date of publication |
Cambridge ; New York : Cambridge University Press, ©1993 |
| International Standard Book Number |
0521458862 |
| Record control number |
(DLC) 94211280 |
| -- |
(OCoLC)29409678 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
London Mathematical Society lecture note series ; |
| Volume number/sequential designation |
190. |
| 9 (RLIN) |
144795 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552411">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552411</a> |
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EBSCOhost |
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EBSC |
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552411 |
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YBP Library Services |
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YANK |
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10405630 |
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92 |
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INOPJ |
