Abstract

Which integer polynomials can we write down if the only exponent to be used is 3? Such problems can be considered as instances of the subnearring generation problem. We show that the nearring (ℤ[x], +, ◦) of integer polynomials, where the nearring multiplication is the composition of polynomials, has uncountably many subnearrings, and we give an explicit description of those nearrings that are generated by subsets of {1, x, x², x³ }.

中文翻译：

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使用函数组合从 X2 和 X3 生成整数多项式：研究 (ℤ[X], +, ◦) 的子近似

摘要

如果要使用的唯一指数是 3，我们可以写出哪些整数多项式？这样的问题可以被认为是亚邻生成问题的实例。我们证明整数多项式的近环 (ℤ[ x ], +, ◦)，其中近环乘法是多项式的组合，有无数个子近环，并且我们给出了由 { 的子集生成的那些近环的明确描述1, x , x ² , x ³ }。