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Value Functions on Simple Algebras, ...
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Tignol, Jean-Pierre.
Value Functions on Simple Algebras, and Associated Graded Rings
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Value Functions on Simple Algebras, and Associated Graded Rings/ by Jean-Pierre Tignol, Adrian R. Wadsworth.
作者:
Tignol, Jean-Pierre.
其他作者:
Wadsworth, Adrian R.
面頁冊數:
XV, 643 p.online resource. :
Contained By:
Springer Nature eBook
標題:
Associative rings. -
電子資源:
https://doi.org/10.1007/978-3-319-16360-4
ISBN:
9783319163604
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. - 1st ed. 2015. - XV, 643 p.online resource. - 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
Standard No.: 10.1007/978-3-319-16360-4doiSubjects--Topical Terms:
893564
Associative rings.
LC Class. No.: QA251.5
Dewey Class. No.: 512.46
Value Functions on Simple Algebras, and Associated Graded Rings
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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.
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