论文标题
在摇滚纸剪裁器代数上评估具有单位在任意场上的岩纸剪辑器代数上评估的多连接多项式的图像
The images of multilinear non-associative polynomials evaluated on a rock-paper-scissors algebra with unit over an arbitrary field
论文作者
论文摘要
令$ {\ mathbb f} $为任意字段。我们考虑岩石，纸张，纸张和剪刀的换向性，非缔合，$ 4 $维代数$ {\ mathfrak m} $，纸张和剪刀超过$ {\ mathbb f} $，我们证明了$ {\ Mathfrak m} $ apassociat $ a andsociat fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomeal fornomial fornomial fornomial and vernomeal fornomial and imial fornomial and v。 空间。我们考虑了两个子代数的同样问题：岩石的代数，纸张和无单位的剪刀，以及一个零标量部分的跟踪零元素的代数。此外，在本文中，我们考虑了这些代数对均质多项式的可能评估问题。
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.
