Geodesic
Immediate Extensions of Pr\"ufer Rings
Algebra i logika, Tome 40 (2001) no. 3, pp. 262-289.

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We study into questions that naturally arise when Prüfer rings are viewed from the geometry standpoint. A ring of principal ideals which has infinitely many prime ideals and is such that its field of fractions is non-Hilbertian is constructed. This answers in the negative a question of Lang.
Keywords: Prüfer ring, ring of principal ideal, field of fractions. 
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     author = {Yu. L. Ershov},
     title = {Immediate {Extensions} of {Pr\"ufer} {Rings}},
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Yu. L. Ershov. Immediate Extensions of Pr\"ufer Rings. Algebra i logika, Tome 40 (2001) no. 3, pp. 262-289. http://geodesic.mathdoc.fr/item/AL_2001_40_3_a1/