LEADER 03171nam 2200577Ia 450 001 9910482998503321 005 20200520144314.0 010 $a3-642-31152-0 024 7 $a10.1007/978-3-642-31152-9 035 $a(CKB)3400000000085875 035 $a(SSID)ssj0000746090 035 $a(PQKBManifestationID)11930881 035 $a(PQKBTitleCode)TC0000746090 035 $a(PQKBWorkID)10860443 035 $a(PQKB)10605900 035 $a(DE-He213)978-3-642-31152-9 035 $a(MiAaPQ)EBC3070544 035 $a(PPN)16532936X 035 $a(EXLCZ)993400000000085875 100 $a20120602d2012 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aPrime divisors and noncommutative valuation theory /$fHidetoshi Marubayashi, Fred Van Oystaeyen 205 $a1st ed. 2012. 210 $aBerlin ;$aHeidelberg $cSpringer$dc2012 215 $a1 online resource (IX, 218 p.) 225 1 $aLecture notes in mathematics,$x1617-9692 ;$v2059 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-31151-2 320 $aIncludes bibliographical references and index. 327 $a1. General Theory of Primes -- 2. Maximal Orders and Primes -- 3. Extensions of Valuations to some Quantized Algebras. 330 $aClassical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves.  But the noncommutative equivalent is mainly applied to finite dimensional skewfields.  Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture.  This arithmetical nature is also present in the theory of maximal orders in central simple algebras.  Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras.  Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized algebras, the development of a theory of Hopf valuations on Hopf algebras and quantum groups, noncommutative valuations on the Weyl field and interesting rings of invariants and valuations of Gauss extensions. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2059. 606 $aNoncommutative rings 606 $aValuation theory 615 0$aNoncommutative rings. 615 0$aValuation theory. 676 $a512.46 686 $a16W40$a16W70$a16S38$a16H10$a13J20$a16T05$2msc 700 $aMarubayashi$b Hidetoshi$f1941-$0477685 701 $aOystaeyen$b F. Van$f1947-$055393 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910482998503321 996 $aPrime divisors and noncommutative valuation theory$93372335 997 $aUNINA