Characterization of field homomorphisms through Pexiderized functional equations

2018/10/29 by Eszter Gselmann, Gselmann, Eszter, Gergely Kiss +3
Mathematics · #13F20 #39B22 #39B62 #39B72 #43A45 #43A70 #Commutative Algebra (math.AC) #FOS: Mathematics #Functional Equations Stability Results #math.AC #msc:13F20 #msc:39B22 #msc:39B62 #msc:39B72 #msc:43A45 #msc:43A70

paper · pdf · doi:10.48550/arxiv.1810.11999

arxiv created 2018/10/29 · openalex publication_date 2018/10/29 · arxiv updated 2018/10/30 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to prove characterization theorems for field homomorphisms. More precisely, the main result investigates the following problem. Let n∈ ℕ be arbitrary, \mathbbK a field and f₁, …, f_n\colon \mathbbK→ ℂ additive functions. Suppose further that equation ∑_i=1ⁿf^q_ii(x^p_i)=0 (x∈ \mathbbK) is also satisfied. Then the functions f₁, …, f_n are linear combinations of field homomorphisms from \mathbbK to ℂ.

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