Aleksander Czarnecki, Maximal ideals in the ring of regulous functions are not finitely generated

The paper consider regulous functions on the real affine space RN. We shall study some algebraic properties of the ring of those functions. It is presented a proof of the regulous version of Nullstellensatz based on the substitution property and the Artin-Lang property for the considered function ring. We prove that every maximal ideal in the ring of regulous functions on RN when N2 is not finitely generated. Finally, we extend the latter result to an arbitrary, smooth, real affine algebraic variety of dimension d2 (copyright: Aleksander Czarnecki)


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