東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Value functions on simple algebras, ...

Tignol, Jean-Pierre.

Linked to FindBook

Google Book

Amazon

博客來

Value functions on simple algebras, and associated graded rings

Record Type:	Electronic resources : Monograph/item
Title/Author:	Value functions on simple algebras, and associated graded rings/ by Jean-Pierre Tignol, Adrian R. Wadsworth.
Author:	Tignol, Jean-Pierre.
other author:	Wadsworth, Adrian R.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xv, 643 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Algebra. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-16360-4
ISBN:	9783319163604 (electronic bk.)

Value functions on simple algebras, and associated graded rings
Tignol, Jean-Pierre.

Value functions on simple algebras, and associated graded rings[electronic resource] /by Jean-Pierre Tignol, Adrian R. Wadsworth. - Cham :Springer International Publishing :2015. - xv, 643 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

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.

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.

ISBN: 9783319163604 (electronic bk.)

Standard No.: 10.1007/978-3-319-16360-4doiSubjects--Topical Terms:

516203
Algebra.

LC Class. No.: QA155

Dewey Class. No.: 512

Value functions on simple algebras, and associated graded rings
LDR:02468nmm m2200325 m 4500 001 2001867
003 DE-He213
005 20151117133234.0
006 m d
007 cr nn 008maaau
008 151215s2015 gw s 0 eng d
020 $a 9783319163604 (electronic bk.)
020 $a 9783319163598 (paper)
024 7 $a 10.1007/978-3-319-16360-4 $2 doi
035 $a 978-3-319-16360-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA155
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 512 $2 23
090 $a QA155 $b .T567 2015
100 1 $a Tignol, Jean-Pierre. $3 713999
245 1 0 $a Value functions on simple algebras, and associated graded rings $h [electronic resource] / $c by Jean-Pierre Tignol, Adrian R. Wadsworth.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xv, 643 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a 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 $a 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 $a Algebra. $3 516203
650 0 $a Rings (Algebra) $3 540500
650 0 $a Valuation theory. $3 532054
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Associative Rings and Algebras. $3 897405
650 2 4 $a Field Theory and Polynomials. $3 891077
700 1 $a Wadsworth, Adrian R. $3 2145796
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 1535313
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-16360-4
950 $a Mathematics and Statistics (Springer-11649)