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Dynamical method in algebra: effective Nullstellensätze

✍ Scribed by Michel Coste; Henri Lombardi; Marie-Françoise Roy

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
363 KB
Volume
111
Category
Article
ISSN
0168-0072

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✦ Synopsis

We give a general method for producing various e ective Null and Positivstellens atze, and getting new Positivstellens atze in algebraically closed valued ÿelds and ordered groups. These various e ective Nullstellens atze produce algebraic identities certifying that some geometric conditions cannot be simultaneously satisÿed. We produce also constructive versions of abstract classical results of algebra based on Zorn's lemma in several cases where such constructive version did not exist. For example, the fact that a real ÿeld can be totally ordered, or the fact that a ÿeld can be embedded in an algebraically closed ÿeld. Our results are based on the concepts we develop of dynamical proofs and simultaneous collapse.

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