000			03124nam a22004935i 4500
001			978-3-319-16360-4
003			DE-He213
005			20161006171606.0
007			cr nn 008mamaa
008			150403s2015 gw | s |||| 0|eng d
020			_a9783319163604 _9978-3-319-16360-4
024	7		_a10.1007/978-3-319-16360-4 _2doi
050		4	_aQA251.5
072		7	_aPBF _2bicssc
072		7	_aMAT002010 _2bisacsh
082	0	4	_a512.46 _223
100	1		_aTignol, Jean-Pierre. _eauthor.
245	1	0	_aValue Functions on Simple Algebras, and Associated Graded Rings _h[electronic resource] / _cby Jean-Pierre Tignol, Adrian R. Wadsworth.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2015.
300			_aXV, 643 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_aValuations 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			_aThis 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	_aMathematics.
650		0	_aAssociative rings.
650		0	_aRings (Algebra).
650		0	_aAlgebra.
650		0	_aField theory (Physics).
650	1	4	_aMathematics.
650	2	4	_aAssociative Rings and Algebras.
650	2	4	_aField Theory and Polynomials.
700	1		_aWadsworth, Adrian R. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319163598
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-319-16360-4
912			_aZDB-2-SMA
999			_c227032 _d227032