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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 ringsby 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.
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:

188312
Algebra.

LC Class. No.: QA155

Dewey Class. No.: 512

Value functions on simple algebras, and associated graded rings
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100 1 $a Tignol, Jean-Pierre. $3 347693
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.
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650 0 $a Rings (Algebra) $3 190979
650 0 $a Valuation theory. $3 296766
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Field Theory and Polynomials. $3 274058
700 1 $a Wadsworth, Adrian R. $3 719772
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 557774
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-16360-4
950 $a Mathematics and Statistics (Springer-11649)