{"product_id":"manis-valuations-and-prufer-extensions-ii-von-tobias-kaiser-manfred-knebusch","title":"Manis Valuations and Prüfer Extensions II","description":"\n                                \n                \u003cp\u003e\n                                        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.\n                    \n                    \u003cbr\u003e\n                                        \n                    \u003cbr\u003e\n                                    \n                \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783319032115\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783319032115","offer_id":39426047213661,"sku":"9783319032115","price":37.44,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/a72fee11-7205-4511-9b24-2b0d28145200.jpg?v=1772084000","url":"https:\/\/shop.autorenwelt.de\/products\/manis-valuations-and-prufer-extensions-ii-von-tobias-kaiser-manfred-knebusch","provider":"Autorenwelt Shop","version":"1.0","type":"link"}