{"product_id":"9783319032115","title":"Manis Valuations and Prüfer Extensions II","description":"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\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePublication Year: \u003c\/strong\u003e2014\u003cbr\u003e\u003cstrong\u003eImprint: \u003c\/strong\u003eSpringer International Publishing\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eFormat: P\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003eWeight (Gram): 3168\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003cbr\u003e\u003cstrong\u003e\u003c\/strong\u003e\u003c\/p\u003e","brand":"Manfred Knebusch","offers":[{"title":"Default Title","offer_id":41272729239730,"sku":"9783319032115","price":54.59,"currency_code":"SGD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0502\/5382\/4178\/products\/3319032119.01_SCLZZZZZZZ.jpg?v=1636127582","url":"https:\/\/readabook.store\/products\/9783319032115","provider":"READABOOK BY ALKEM","version":"1.0","type":"link"}