MARC details
| 000 -LEADER |
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| fixed length control field |
02278 a2200265 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319163598 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA155 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512 |
| 090 ## - LOCALLY ASSIGNED LC-TYPE CALL NUMBER (OCLC); LOCAL CALL NUMBER (RLIN) |
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| -- |
31578 |
| -- |
31578 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Tignol, Jean-Pierre |
| 245 10 - TITLE STATEMENT |
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| Title |
Value functions on simple algebras, and associated graded rings |
| Statement of responsibility, etc. |
Jean-Pierre Tignol, Adrian R. Wadworth |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
|---|
| Place of publication, distribution, etc. |
heidelberg, New York, Dordrecht: |
| Name of publisher, distributor, etc. |
Springer |
| Date of publication, distribution, etc. |
2015 |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
644 p. |
| Dimensions |
24 cm |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Springer Monographs in Mathematics |
| 546 ## - LANGUAGE NOTE |
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| Language note |
eng |
| 500 ## - GENERAL NOTE |
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| General note |
Bibliografie p. 621<br/>Index p. 635<br/>Cuprinde Exercitii si Note la sfarsitul fiecarui capitol |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Valuations on Division Rings -- Graded Algebra -- Value Functions -- Existence and Fundamental Properties of Gauges -- Graded and Valued Field Extensions -- Brauer Groups -- Total Ramifcation -- Division Algebras over Henselian Fields -- Subfields and Splitting Fields of Division Algebras -- Indecomposable Division Algebras -- Computation of SK1(D) -- The Essential Dimension of Central Simple Algebras. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of noncrossed products and Platonov's solution of the Tannaka-Artin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Algebra |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Rings (Algebra) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Valuation theory |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Wadsworth, Adrian R. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Springer Monographs in Mathematics |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Institution code [OBSOLETE] |
IMAR |
| Koha item type |
Carti |
| Call number prefix |
512 |
| Serial record flag |
EP |