By Manfred Knebusch
The current publication is dedicated to a examine of relative Prüfer jewelry and Manis valuations, with a watch to program in genuine and p-adic geometry. If one desires to extend at the traditional algebraic geometry over a non-algebraically closed base box, e.g. a true closed box or p-adically closed box, one normally meets plenty of valuation domain names. frequently they aren't discrete and for that reason no longer noetherian. hence, for another develomemt of actual algebraic and genuine analytic geometry particularly, and definitely additionally inflexible analytic and p-adic geometry, new chapters of commutative algebra are wanted, usually of a non-noetherian nature. the current quantity offers one such bankruptcy.
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