A nullstellensatz for ordered fields

Abstract

For an ordered field k, a realzero of an ideal P in the polynomial ring kwhere k is the realclosure of k, the realvariety ~e'n (p) is the set of all realzeros of P, and, as usual, J(G), for any subset G of ~(n) is the ideal of all members of k[X] that vanish all over G. Our nullstellensatz asserts: B J~CfR (P) = VP = realradical of P, R where I/ff is the set of all/(X) such that for some exponent m, some rational functions u,(X) in k(X), and positive p~ ek

Locations

• Arkiv för matematik - View - PDF