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arXiv · 1706.07862

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

Aleksander Czarnecki
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Abstract

The paper consider regulous functions on the real affine space $\mathbb{R}^N$. 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 $\mathbb{R}^N$ when $N\geq 2$ is not finitely generated. Finally, we extend the latter result to an arbitrary, smooth, real affine algebraic variety of dimension $d\geq 2$.

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Aleksander Czarnecki. 2017-06-23. Maximal ideals in the ring of regulous functions are not finitely generated. https://arxiv.org/abs/1706.07862

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