Mathieu-Zhao spaces of polynomial rings

2019/07/13 by Arno van den Essen, Essen, Arno van den, Loes van Hove +1
Mathematics · #13C99 #13F20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Meromorphic and Entire Functions #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1907.06106

openalex publication_date 2019/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe all Mathieu-Zhao spaces of k[x₁,⋯,x_n] (k is an algebraically closed field of characteristic zero) which contains an ideal of finite codimension. Furthermore we give an algorithm to decide if a subspace of the form I+kv₁+⋯+kv_r is a Mathieu-Zhao space, in case the ideal I has finite codimension.

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