论文标题
C* - 代数casas-alvero猜想
C*-algebraic Casas-Alvero Conjecture
论文作者
论文摘要
基于casas-alvero猜想\ textit {[j。代数，2001]}我们制定以下猜想。 （z-a_n）$是$ \ mathcal {a} $的多项式，带有$ a_1，a_2，\ dots，a_n \ in \ mathcal {a} $。如果$ p $与其每个（第一个）$ n-1 $衍生物中的每个（第一个）$ n^\ text {th} $线性c*-algebraic多项式的功率。
Based on Casas-Alvero conjecture \textit{[J. Algebra, 2001]} we formulate the following conjecture.\\ \textbf{C*-algebraic Casas-Alvero Conjecture : Let $\mathcal{A}$ be a commutative C*-algebra, $n\in \mathbb{N}$ and let $P(z) = (z-a_1)(z-a_2)\cdots (z-a_n)$ be a polynomial over $\mathcal{A}$ with $a_1, a_2, \dots, a_n \in \mathcal{A}$. If $P$ shares a common zero with each of its (first) $n-1$ derivatives, then it is $n^\text{th}$ power of a linear monic C*-algebraic polynomial.}\\ We show that C*-algebraic Casas-Alvero Conjecture holds for C*-algebraic polynomials of degree 2.
