000 | 03052nam a22005175i 4500 | ||
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001 | 978-3-642-31152-9 | ||
003 | DE-He213 | ||
005 | 20140220083321.0 | ||
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 |
|
082 | 0 | 4 |
_a512 _223 |
100 | 1 |
_aMarubayashi, Hidetoshi. _eauthor. |
|
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 |
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337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
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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 | _aMathematics. | |
650 | 0 | _aAlgebra. | |
650 | 0 | _aGeometry, algebraic. | |
650 | 0 | _aGeometry. | |
650 | 1 | 4 | _aMathematics. |
650 | 2 | 4 | _aAlgebra. |
650 | 2 | 4 | _aGeometry. |
650 | 2 | 4 | _aAlgebraic Geometry. |
650 | 2 | 4 | _aAssociative Rings and Algebras. |
700 | 1 |
_aVan Oystaeyen, Fred. _eauthor. |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783642311512 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2059 |
|
856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-642-31152-9 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c103309 _d103309 |