Titlebook: Value Functions on Simple Algebras, and Associated Graded Rings; Jean-Pierre Tignol,Adrian R. Wadsworth Book 2015 Springer International P

極小

Jean-Pierre Tignol,Adrian R. Wadsworthd the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley‘s book, ‘The Algebraic Theory 978-94-010-8602-8978-94-009-4728-3Series ISSN 1389-2185

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Brauer Groups,aded field. This result is fundamental for the use of graded algebras to study division algebras over Henselian fields. An application is given to obtain a split exact sequence for the inertially split part of the Brauer group of a Henselian field. Another application of the theorem yields Witt’s de

membrane

Total Ramification, graded field (i.e., .. is separably closed), we prove a group isomorphism from .(.) to the part of . of torsion prime to . mapping ., where . is the canonical pairing induced by commutators. For . not inertially closed, this leads to a description of .(.)/..(.) as a subgroup of . determined by the

雪崩

Division Algebras over Henselian Fields,. is inertially split and . is tame and totally ramified over .. We show further that every inertially split division algebra . is Brauer equivalent to some .?.., where . is inertial over . and . is decomposably semiramified. The classes . for the . appearing in the .?.. decompositions of . are show

Anthrp

Indecomposable Division Algebras,elds examples of exponent?2 and degree?8 in ?§., and of exponent?.≠2 and degree .. with .≥2 in §.. The last section, §., deals with complete decompositions into tensor products of symbol algebras. The main result is Th.?., which relates armatures in an inertially split division algebra over a Hensel

Fortuitous

The Essential Dimension of Central Simple Algebras,hen in §. we sketch their method to obtain lower bounds on the essential .-dimension of central simple algebras. In the final §., we discuss consequences of these lower bounds for the decomposability of division algebras into tensor products of symbol algebras.

Libido

Book 2015ecomposable 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..