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Pillars and towers of quadratic transformations. (English) Zbl 1227.14004

A field \(k\) has the kroneckerian dimension \(n\) if its transcendence degree over its prime subfield is either \(n\) if char \(k>0\), or \(n+1\) otherwise. For any field \(k\) of kroneckerian dimension \(n\) there exists a subring \(A\) of \({\mathbb Z}[T_1,\ldots, T_{n+1}]\) such that \(k\) is a factor ring of \(A\). The proof uses the so called infinite pillars of quadratic transformations. Towers whose underlying quadratic transformations are finite pillars or nonpillars are employed for the construction of basic dicritical divisors.

MSC:

14A05 Relevant commutative algebra
13H05 Regular local rings
13F30 Valuation rings
14C20 Divisors, linear systems, invertible sheaves
Full Text: DOI

References:

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