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

2017/06/23 by Aleksander Czarnecki, Czarnecki, Aleksander
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1706.07862

openalex publication_date 2017/06/23 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28

Abstract

The paper consider regulous functions on the real affine space\n\ℝ^N. We shall study some algebraic properties of the ring of those\nfunctions. It is presented a proof of the regulous version of Nullstellensatz\nbased on the substitution property and the Artin-Lang property for the\nconsidered function ring. We prove that every maximal ideal in the ring of\nregulous functions on \ℝ^N when N\≥ 2 is not finitely generated.\nFinally, we extend the latter result to an arbitrary, smooth, real affine\nalgebraic variety of dimension d\≥ 2.\n

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