000 03445nam a22005175i 4500
001 978-3-642-31152-9
003 DE-He213
005 20190213151701.0
007 cr nn 008mamaa
008 120821s2012 gw | s |||| 0|eng d
020 _a9783642311529
_9978-3-642-31152-9
024 7 _a10.1007/978-3-642-31152-9
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aMarubayashi, Hidetoshi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aPrime Divisors and Noncommutative Valuation Theory
_h[electronic resource] /
_cby Hidetoshi Marubayashi, Fred Van Oystaeyen.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2012.
300 _aIX, 218 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2059
505 0 _a1. General Theory of Primes -- 2. Maximal Orders and Primes -- 3. Extensions of Valuations to some Quantized Algebras.
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.
650 0 _aAlgebra.
650 0 _aGeometry.
650 0 _aGeometry, algebraic.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aAssociative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11027
700 1 _aVan Oystaeyen, Fred.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642311512
776 0 8 _iPrinted edition:
_z9783642311536
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2059
856 4 0 _uhttps://doi.org/10.1007/978-3-642-31152-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11530
_d11530