论文标题
添加函数的多项式方程I。内部情况
Polynomial equations for additive functions I. The inner case
论文作者
论文摘要
这项工作序列的目的是研究通过加性函数满足的多项式方程。因此，可以给出针对同构和衍生的新特征定理。更准确地说，在本文中，考虑以下类型的方程式被认为$ \ sum_ {i = 1}^{n} f_ {i}（x^{p_ {p_ {i}}）g_ {i}（x^{q_ {q_ {q_ {i}}} integer，$ \ mathbb {f} \ subset \ mathbb {c} $是一个字段，$ f_ {i}，g_ {i} \ colon \ mathbb {f} \ to \ mathbb {c} c} c} c {c} $是附加功能，$ p_i，q_i $ le $ $ $ $ $ $ yd $ i = 1 = 1 = 1 = 1 = 1 = 1。
The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the following type of equation is considered $$\sum_{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x^{q_{i}})= 0 \qquad \left(x\in \mathbb{F}\right),$$ where $n$ is a positive integer, $\mathbb{F}\subset \mathbb{C}$ is a field, $f_{i}, g_{i}\colon \mathbb{F}\to \mathbb{C}$ are additive functions and $p_i, q_i$ are positive integers for all $i=1, \ldots, n$.
