03324nam 22005535 450 99620327660331620200704123148.03-319-03212-710.1007/978-3-319-03212-2(CKB)3710000000094973(DE-He213)978-3-319-03212-2(SSID)ssj0001187318(PQKBManifestationID)11753657(PQKBTitleCode)TC0001187318(PQKBWorkID)11257233(PQKB)10003889(MiAaPQ)EBC3107078(PPN)177824387(EXLCZ)99371000000009497320140320d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierManis Valuations and Prüfer Extensions II[electronic resource] /by Manfred Knebusch, Tobias Kaiser1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (XII, 190 p.) Lecture Notes in Mathematics,0075-8434 ;2103Bibliographic Level Mode of Issuance: Monograph3-319-03211-9 Overrings and PM-Spectra -- Approximation Theorems -- Kronecker extensions and star operations -- Basics on Manis valuations and Prufer extensions -- Multiplicative ideal theory -- PM-valuations and valuations of weaker type -- Overrings and PM-Spectra -- Approximation Theorems -- Kronecker extensions and star operations -- Appendix -- References -- Index.This volume is a sequel to “Manis Valuation and Prüfer Extensions I,” LNM1791. The Prüfer extensions of a commutative ring A are roughly those commutative ring extensions R / A,where commutative algebra is governed by Manis valuations on R with integral values on A. These valuations then turn out to belong to the particularly amenable subclass of PM (=Prüfer-Manis) valuations. While in Volume I Prüfer extensions in general and individual PM valuations were studied, now the focus is on families of PM valuations. One highlight is the presentation of a very general and deep approximation theorem for PM valuations, going back to Joachim Gräter’s work in 1980, a far-reaching extension of the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called “Kronecker extensions,” where PM valuations are put to use in  arbitrary commutative  ring extensions in a way that ultimately goes back to the work of Leopold Kronecker.Lecture Notes in Mathematics,0075-8434 ;2103Commutative algebraCommutative ringsCommutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Commutative algebra.Commutative rings.Commutative Rings and Algebras.512.4413A1813A1513F0513F3013B3011J61mscKnebusch Manfredauthttp://id.loc.gov/vocabulary/relators/aut54845Kaiser Tobiasauthttp://id.loc.gov/vocabulary/relators/autBOOK996203276603316Manis Valuations and Prüfer Extensions II2354908UNISA