任意域上带单位的石头剪刀布代数上的多线性非结合多项式的象
The images of multilinear non-associative polynomials evaluated on a rock-paper-scissors algebra with unit over an arbitrary field
摘要：
设${\mathbb F}$为任意字段。本文考虑交换的、非结合的、$4$ -维代数${\mathfrak M}$的岩石，纸和剪刀与单位在${\mathbb F}$和我们证明了图像在${\mathfrak M}$的每一个非结合的多线性多项式在${\mathbb F}$是一个向量空间。同样的问题，我们考虑两个子代数：一个代数的岩石，纸和剪刀没有单位，和代数的迹零元素零标量部分。此外，本文还考虑了这些代数上的齐次多项式的可能求值问题。
英文摘要：
Let ${\mathbb F}$ be an arbitrary field. We consider a commutative, non-associative, $4$-dimensional algebra ${\mathfrak M}$ of the rock, the paper and the scissors with unit over ${\mathbb F}$ and we prove that the image over ${\mathfrak M}$ of every non-associative multilinear polynomial over ${\mathbb F}$ is a vector space. The same question we consider for two subalgebras: an algebra of the rock, the paper and the scissors without unit, and an algebra of trace zero elements with zero scalar part. Moreover in this paper we consider the questions of possible evaluations of homogeneous polynomials on these algebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
