03805nam 22006735 450 991029976640332120200705010729.03-319-16360-410.1007/978-3-319-16360-4(CKB)3710000000387656(EBL)2096706(SSID)ssj0001498322(PQKBManifestationID)11837666(PQKBTitleCode)TC0001498322(PQKBWorkID)11501524(PQKB)10639177(DE-He213)978-3-319-16360-4(MiAaPQ)EBC2096706(PPN)185489702(EXLCZ)99371000000038765620150403d2015 u| 0engur|n|---|||||txtccrValue Functions on Simple Algebras, and Associated Graded Rings /by Jean-Pierre Tignol, Adrian R. Wadsworth1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (652 p.)Springer Monographs in Mathematics,1439-7382Description based upon print version of record.3-319-16359-0 Includes bibliographical references and index.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.Springer Monographs in Mathematics,1439-7382Associative ringsRings (Algebra)AlgebraField theory (Physics)Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Field Theory and Polynomialshttps://scigraph.springernature.com/ontologies/product-market-codes/M11051Associative rings.Rings (Algebra)Algebra.Field theory (Physics)Associative Rings and Algebras.Field Theory and Polynomials.512.4Tignol Jean-Pierreauthttp://id.loc.gov/vocabulary/relators/aut49824Wadsworth Adrian Rauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299766403321Value Functions on Simple Algebras, and Associated Graded Rings2546581UNINA