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Minimal pairs for P

✍ Scribed by Uwe Schöning

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
782 KB
Volume
31
Category
Article
ISSN
0304-3975

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A P-matrix is a square matrix with positive principal minors. We introduce a natural extension of the class of P-matrices, the class of extended P-pairs. A pair {I, M}, for a P-matrix M, is shown to be contained in an extended P-pair iff SMS has an n-step vector for some sign matrix S. Such a matrix

Cell decomposition for P-minimal fields
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✍ Marie-Hélène Mourgues 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 92 KB

## Abstract In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for __p__‐adically closed fields. We work here with the notion of __P__‐minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a __P__‐minimal field __K__ admits cell decomposition if an