Prime Divisors and Noncommutative Valuation Theory (Record no. 11530)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03445nam a22005175i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-642-31152-9 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20190213151701.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 120821s2012 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783642311529 |
| -- | 978-3-642-31152-9 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-642-31152-9 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA150-272 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBF |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT002000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBF |
| Source | thema |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Marubayashi, Hidetoshi. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 245 10 - TITLE STATEMENT | |
| Title | Prime Divisors and Noncommutative Valuation Theory |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by Hidetoshi Marubayashi, Fred Van Oystaeyen. |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg : |
| -- | Imprint: Springer, |
| -- | 2012. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | IX, 218 p. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Lecture Notes in Mathematics, |
| International Standard Serial Number | 0075-8434 ; |
| Volume number/sequential designation | 2059 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. General Theory of Primes -- 2. Maximal Orders and Primes -- 3. Extensions of Valuations to some Quantized Algebras. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture. This arithmetical nature is also present in the theory of maximal orders in central simple algebras. Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras. Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized algebras, the development of a theory of Hopf valuations on Hopf algebras and quantum groups, noncommutative valuations on the Weyl field and interesting rings of invariants and valuations of Gauss extensions. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebra. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Geometry, algebraic. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebra. |
| -- | http://scigraph.springernature.com/things/product-market-codes/M11000 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Geometry. |
| -- | http://scigraph.springernature.com/things/product-market-codes/M21006 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebraic Geometry. |
| -- | http://scigraph.springernature.com/things/product-market-codes/M11019 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Associative Rings and Algebras. |
| -- | http://scigraph.springernature.com/things/product-market-codes/M11027 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Van Oystaeyen, Fred. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783642311512 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783642311536 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Lecture Notes in Mathematics, |
| -- | 0075-8434 ; |
| Volume number/sequential designation | 2059 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.1007/978-3-642-31152-9 |
| 912 ## - | |
| -- | ZDB-2-SMA |
| 912 ## - | |
| -- | ZDB-2-LNM |
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