000060913 001__ 60913
000060913 005__ 20140222003229.0
000060913 0248_ $$2doi$$a10.1007/978-3-642-31152-9
000060913 020__ $$9978-3-642-31152-9$$a9783642311529
000060913 050_4 $$aQA150-272
000060913 072_7 $$2bicssc$$aPBF
000060913 072_7 $$2bisacsh$$aMAT002000
000060913 08204 $$223$$a512
000060913 100__ $$aMarubayashi, Hidetoshi.
000060913 245__ $$aPrime Divisors and Noncommutative Valuation Theory$$cby Hidetoshi Marubayashi, Fred Van Oystaeyen.$$h[electronic resource] /
000060913 260__ $$aBerlin, Heidelberg :$$bImprint: Springer,$$bSpringer Berlin Heidelberg :$$c2012.
000060913 300__ $$aIX, 218 p.$$bdigital.
000060913 490__ $$aLecture Notes in Mathematics,$$v2059$$x0075-8434 ;
000060913 5050_ $$a1. General Theory of Primes -- 2. Maximal Orders and Primes -- 3. Extensions of Valuations to some Quantized Algebras.
000060913 520__ $$aClassical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves.  But the noncommutative equivalent is mainly applied to finite dimensional skewfields.  Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture.  This arithmetical nature is also present in the theory of maximal orders in central simple algebras.  Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras.  Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized algebras, the development of a theory of Hopf valuations on Hopf algebras and quantum groups, noncommutative valuations on the Weyl field and interesting rings of invariants and valuations of Gauss extensions.
000060913 65017 $$aMathematics.
000060913 65017 $$aAlgebra.
000060913 65017 $$aGeometry, algebraic.
000060913 65017 $$aGeometry.
000060913 65027 $$aMathematics.
000060913 65027 $$aAlgebra.
000060913 65027 $$aGeometry.
000060913 65027 $$aAlgebraic Geometry.
000060913 65027 $$aAssociative Rings and Algebras.
000060913 700__ $$aVan Oystaeyen, Fred.
000060913 710__ $$aSpringerLink (Online service)
000060913 710__ $$tSpringer eBooks
000060913 77608 $$iPrinted edition:$$z9783642311512
000060913 830_0 $$aLecture Notes in Mathematics,$$v2059$$x0075-8434 ;
000060913 8564_ $$uhttp://dx.doi.org/10.1007/978-3-642-31152-9
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000060913 912__ $$aZDB-2-SMA
000060913 912__ $$aZDB-2-LNM
000060913 950__ $$aMathematics and Statistics (Springer-11649)
000060913 980__ $$aBOOK